{
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "manuscripts": [
    {
      "manuscript_id": "001:Milnes-rationality-conjecture-for-abelian-varieties-October-7-2026",
      "family_id": "001",
      "discipline": "Number theory",
      "title": "Milne's rationality conjecture for abelian varieties",
      "pdf_path": "preprints/Milnes-rationality-conjecture-for-abelian-varieties-October-7-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Milnes-rationality-conjecture-for-abelian-varieties-October-7-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "002:Exact-Birch-Swinnerton-Dyer-Formula-from-Low-Selmer-Corank-October-7-2026",
      "family_id": "002",
      "discipline": "Number theory",
      "title": "Exact Birch\u2013Swinnerton-Dyer Formula from Low Selmer Corank",
      "pdf_path": "preprints/Exact-Birch-Swinnerton-Dyer-Formula-from-Low-Selmer-Corank-October-7-2026/exact-bsd-low-selmer-corank.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-Birch-Swinnerton-Dyer-Formula-from-Low-Selmer-Corank-October-7-2026/exact-bsd-low-selmer-corank.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "002:The-Selmer-converse-for-elliptic-curves-at-every-prime-October-7-2026",
      "family_id": "002",
      "discipline": "Number theory",
      "title": "The Selmer converse for elliptic curves at every prime",
      "pdf_path": "preprints/The-Selmer-converse-for-elliptic-curves-at-every-prime-October-7-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Selmer-converse-for-elliptic-curves-at-every-prime-October-7-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "002:The-two-primary-Birch-Swinnerton-Dyer-formula-in-Selmer-corank-at-most-one-October-6-2026",
      "family_id": "002",
      "discipline": "Number theory",
      "title": "The two-primary Birch\u2013Swinnerton-Dyer formula in Selmer corank at most one",
      "pdf_path": "preprints/The-two-primary-Birch-Swinnerton-Dyer-formula-in-Selmer-corank-at-most-one-October-6-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-two-primary-Birch-Swinnerton-Dyer-formula-in-Selmer-corank-at-most-one-October-6-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "003:The-Quasi-Riemann-Hypothesis-September-30-2026",
      "family_id": "003",
      "discipline": "Number theory",
      "title": "The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane $`\\Re s\\gt 7/8`$ ",
      "pdf_path": "preprints/The-Quasi-Riemann-Hypothesis-September-30-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Quasi-Riemann-Hypothesis-September-30-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/003.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "003:The-Quasi-Riemann-Hypothesis-October-5-2026",
      "family_id": "003",
      "discipline": "Number theory",
      "title": "The Quasi-Riemann Hypothesis (alternate 11/12 proof)",
      "pdf_path": "preprints/The-Quasi-Riemann-Hypothesis-October-5-2026/paper2.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Quasi-Riemann-Hypothesis-October-5-2026/paper2.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/003.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "003:Uniform-exclusion-of-Landau-Siegel-zeros-October-1-2026",
      "family_id": "003",
      "discipline": "Number theory",
      "title": "Uniform exclusion of Landau\u2013Siegel zeros",
      "pdf_path": "preprints/Uniform-exclusion-of-Landau-Siegel-zeros-October-1-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-exclusion-of-Landau-Siegel-zeros-October-1-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/003.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "004:Hilberts-tenth-problem-over-the-rational-numbers-October-6-2026",
      "family_id": "004",
      "discipline": "Number theory",
      "title": "Hilbert\u2019s tenth problem over the rational numbers",
      "pdf_path": "preprints/Hilberts-tenth-problem-over-the-rational-numbers-October-6-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Hilberts-tenth-problem-over-the-rational-numbers-October-6-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "004:A-pointwise-2-converse-for-elliptic-curves-with-rational-two-torsion-October-7-2026",
      "family_id": "004",
      "discipline": "Number theory",
      "title": "A pointwise 2-converse for elliptic curves with rational two-torsion",
      "pdf_path": "preprints/A-pointwise-2-converse-for-elliptic-curves-with-rational-two-torsion-October-7-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-pointwise-2-converse-for-elliptic-curves-with-rational-two-torsion-October-7-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "005:Catalans-constant-is-irrational-September-24-2026",
      "family_id": "005",
      "discipline": "Number theory",
      "title": "Catalan's constant is irrational",
      "pdf_path": "preprints/Catalans-constant-is-irrational-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Catalans-constant-is-irrational-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/005.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "006:Goldfelds-analytic-density-conjecture-and-the-2-converse-for-elliptic-curves-October-7-2026",
      "family_id": "006",
      "discipline": "Number theory",
      "title": "Goldfeld's analytic density conjecture and the 2-converse for elliptic curves",
      "pdf_path": "preprints/Goldfelds-analytic-density-conjecture-and-the-2-converse-for-elliptic-curves-October-7-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Goldfelds-analytic-density-conjecture-and-the-2-converse-for-elliptic-curves-October-7-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "006:The-mean-analytic-rank-of-quadratic-twists-of-elliptic-curves-October-6-2026",
      "family_id": "006",
      "discipline": "Number theory",
      "title": "The mean analytic rank of quadratic twists of elliptic curves",
      "pdf_path": "preprints/The-mean-analytic-rank-of-quadratic-twists-of-elliptic-curves-October-6-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-mean-analytic-rank-of-quadratic-twists-of-elliptic-curves-October-6-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "007:Ordinary-two-point-correlations-of-multiplicative-functions-September-24-2026",
      "family_id": "007",
      "discipline": "Number theory",
      "title": "Ordinary two-point correlations of multiplicative functions",
      "pdf_path": "preprints/Ordinary-two-point-correlations-of-multiplicative-functions-September-24-2026/final.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Ordinary-two-point-correlations-of-multiplicative-functions-September-24-2026/final.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/007.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "008:The-Deligne-Drinfeld-conjecture-September-23-2026",
      "family_id": "008",
      "discipline": "Number theory",
      "title": "The Deligne-Drinfeld conjecture",
      "pdf_path": "preprints/The-Deligne-Drinfeld-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Deligne-Drinfeld-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/008.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "009:Reconstruction-of-Function-Fields-from-Mod-ell-Milnor-K-Theory-October-5-2026",
      "family_id": "009",
      "discipline": "Number theory",
      "title": "Reconstruction of Function Fields from Mod-\u2113 Milnor K-Theory",
      "pdf_path": "preprints/Reconstruction-of-Function-Fields-from-Mod-ell-Milnor-K-Theory-October-5-2026/mod-ell-bogomolov-pop.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Reconstruction-of-Function-Fields-from-Mod-ell-Milnor-K-Theory-October-5-2026/mod-ell-bogomolov-pop.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/009.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "009:Reconstruction-from-Milnor-K-theory-modulo-the-characteristic-October-5-2026",
      "family_id": "009",
      "discipline": "Number theory",
      "title": "Reconstruction from Milnor K-theory modulo the characteristic",
      "pdf_path": "preprints/Reconstruction-from-Milnor-K-theory-modulo-the-characteristic-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Reconstruction-from-Milnor-K-theory-modulo-the-characteristic-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/009.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "009:The-Bogomolov-Pop-reconstruction-theorem-September-23-2026",
      "family_id": "009",
      "discipline": "Number theory",
      "title": "The Bogomolov-Pop reconstruction theorem",
      "pdf_path": "preprints/The-Bogomolov-Pop-reconstruction-theorem-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Bogomolov-Pop-reconstruction-theorem-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/009.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "010:Unrestricted-pro-modularity-at-the-prime-two-October-6-2026",
      "family_id": "010",
      "discipline": "Number theory",
      "title": "Unrestricted pro-modularity at the prime two",
      "pdf_path": "preprints/Unrestricted-pro-modularity-at-the-prime-two-October-6-2026/two-adic-promodularity.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unrestricted-pro-modularity-at-the-prime-two-October-6-2026/two-adic-promodularity.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "010:The-Dimension-of-the-Two-Adic-Hecke-Algebra-at-Odd-Level-October-5-2026",
      "family_id": "010",
      "discipline": "Number theory",
      "title": "The Dimension of the Two-Adic Hecke Algebra at Odd Level",
      "pdf_path": "preprints/The-Dimension-of-the-Two-Adic-Hecke-Algebra-at-Odd-Level-October-5-2026/two-adic-hecke.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Dimension-of-the-Two-Adic-Hecke-Algebra-at-Odd-Level-October-5-2026/two-adic-hecke.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "010:Fontaine-Mazur-modularity-at-the-prime-2-October-6-2026",
      "family_id": "010",
      "discipline": "Number theory",
      "title": "Fontaine\u2013Mazur modularity at the prime 2",
      "pdf_path": "preprints/Fontaine-Mazur-modularity-at-the-prime-2-October-6-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Fontaine-Mazur-modularity-at-the-prime-2-October-6-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "011:Weighted-Dilation-Graphs-Smooth-Shifted-Primes-and-Totient-Fibers-September-24-2026",
      "family_id": "011",
      "discipline": "Number theory",
      "title": "Weighted dilation graphs, smooth shifted primes and totient fibers",
      "pdf_path": "preprints/Weighted-Dilation-Graphs-Smooth-Shifted-Primes-and-Totient-Fibers-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weighted-Dilation-Graphs-Smooth-Shifted-Primes-and-Totient-Fibers-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "011:The-Poisson-Dirichlet-Law-for-Prime-Predecessors-September-24-2026",
      "family_id": "011",
      "discipline": "Number theory",
      "title": "The Poisson-Dirichlet law for prime predecessors",
      "pdf_path": "preprints/The-Poisson-Dirichlet-Law-for-Prime-Predecessors-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Poisson-Dirichlet-Law-for-Prime-Predecessors-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "011:Prime-Predecessors-with-an-Even-Number-of-Prime-Factors-September-17-2026",
      "family_id": "011",
      "discipline": "Number theory",
      "title": "Prime Predecessors with an Even Number of Prime Factors",
      "pdf_path": "preprints/Prime-Predecessors-with-an-Even-Number-of-Prime-Factors-September-17-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Prime-Predecessors-with-an-Even-Number-of-Prime-Factors-September-17-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "012:The-joint-Dickman-law-for-consecutive-integers-September-24-2026",
      "family_id": "012",
      "discipline": "Number theory",
      "title": "The joint Dickman law for consecutive integers",
      "pdf_path": "preprints/The-joint-Dickman-law-for-consecutive-integers-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-joint-Dickman-law-for-consecutive-integers-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/012.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "013:the-additive-indecomposability-of-the-primes-September-24-2026",
      "family_id": "013",
      "discipline": "Number theory",
      "title": "The additive indecomposability of the primes",
      "pdf_path": "preprints/the-additive-indecomposability-of-the-primes-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/the-additive-indecomposability-of-the-primes-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/013.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "014:Global-Arthur-Enhancements-of-Cuspidal-Excursion-Parameters-October-5-2026",
      "family_id": "014",
      "discipline": "Number theory",
      "title": "Global Arthur Enhancements of Cuspidal Excursion Parameters",
      "pdf_path": "preprints/Global-Arthur-Enhancements-of-Cuspidal-Excursion-Parameters-October-5-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Arthur-Enhancements-of-Cuspidal-Excursion-Parameters-October-5-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "014:Rationality-of-the-Canonical-Unramified-Arthur-Filtration-September-24-2026",
      "family_id": "014",
      "discipline": "Number theory",
      "title": "Rationality of the Canonical Unramified Arthur Filtration",
      "pdf_path": "preprints/Rationality-of-the-Canonical-Unramified-Arthur-Filtration-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Rationality-of-the-Canonical-Unramified-Arthur-Filtration-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "014:Ramanujan-Arthur-Decompositions-of-Cuspidal-Functions-at-Full-Finite-Level-September-24-2026",
      "family_id": "014",
      "discipline": "Number theory",
      "title": "Ramanujan-Arthur Decompositions of Cuspidal Functions at Full Finite Level",
      "pdf_path": "preprints/Ramanujan-Arthur-Decompositions-of-Cuspidal-Functions-at-Full-Finite-Level-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Ramanujan-Arthur-Decompositions-of-Cuspidal-Functions-at-Full-Finite-Level-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "014:Temperedness-at-ramified-places-for-globally-generic-exceptional-groups-October-5-2026",
      "family_id": "014",
      "discipline": "Number theory",
      "title": "Temperedness at ramified places for globally generic exceptional groups",
      "pdf_path": "preprints/Temperedness-at-ramified-places-for-globally-generic-exceptional-groups-October-5-2026/ramified-ramanujan.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Temperedness-at-ramified-places-for-globally-generic-exceptional-groups-October-5-2026/ramified-ramanujan.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "014:The-Restricted-Geometric-Langlands-Equivalence-in-Positive-Characteristic-September-24-2026",
      "family_id": "014",
      "discipline": "Number theory",
      "title": "The Restricted Geometric Langlands Equivalence in Positive Characteristic",
      "pdf_path": "preprints/The-Restricted-Geometric-Langlands-Equivalence-in-Positive-Characteristic-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Restricted-Geometric-Langlands-Equivalence-in-Positive-Characteristic-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "014:Constructible-tame-Hecke-eigensheaves-in-positive-characteristic-October-5-2026",
      "family_id": "014",
      "discipline": "Number theory",
      "title": "Constructible tame Hecke eigensheaves in positive characteristic",
      "pdf_path": "preprints/Constructible-tame-Hecke-eigensheaves-in-positive-characteristic-October-5-2026/constructible-tame-hecke-eigensheaves-positive-characteristic.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Constructible-tame-Hecke-eigensheaves-in-positive-characteristic-October-5-2026/constructible-tame-hecke-eigensheaves-positive-characteristic.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "014:Tame-Hecke-Eigensheaves-with-Several-Marked-Points-October-5-2026",
      "family_id": "014",
      "discipline": "Number theory",
      "title": "Tame Hecke Eigensheaves with Several Marked Points",
      "pdf_path": "preprints/Tame-Hecke-Eigensheaves-with-Several-Marked-Points-October-5-2026/Tame-Hecke-Eigensheaves-with-Several-Marked-Points.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Tame-Hecke-Eigensheaves-with-Several-Marked-Points-October-5-2026/Tame-Hecke-Eigensheaves-with-Several-Marked-Points.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "014:Frobenius-Structures-on-Tame-Hecke-Eigensheaves-October-5-2026",
      "family_id": "014",
      "discipline": "Number theory",
      "title": "Frobenius Structures on Tame Hecke Eigensheaves",
      "pdf_path": "preprints/Frobenius-Structures-on-Tame-Hecke-Eigensheaves-October-5-2026/tame-hecke-frobenius.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Frobenius-Structures-on-Tame-Hecke-Eigensheaves-October-5-2026/tame-hecke-frobenius.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "015:Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026",
      "family_id": "015",
      "discipline": "Number theory",
      "title": "Equidistribution of Prime-Degree Torus Packets with Arbitrary Local Type",
      "pdf_path": "preprints/Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/015.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "015:Equidistribution-of-Primitive-Quartic-Torus-Packets-for-Arbitrary-Orders-October-5-2026",
      "family_id": "015",
      "discipline": "Number theory",
      "title": "Equidistribution of primitive quartic torus packets for arbitrary orders",
      "pdf_path": "preprints/Equidistribution-of-Primitive-Quartic-Torus-Packets-for-Arbitrary-Orders-October-5-2026/quartic-torus-packets.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equidistribution-of-Primitive-Quartic-Torus-Packets-for-Arbitrary-Orders-October-5-2026/quartic-torus-packets.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/015.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "015:Equidistribution-of-Primitive-Sextic-Torus-Packets-October-5-2026",
      "family_id": "015",
      "discipline": "Number theory",
      "title": "Equidistribution of Primitive Sextic Torus Packets",
      "pdf_path": "preprints/Equidistribution-of-Primitive-Sextic-Torus-Packets-October-5-2026/primitive-sextic-torus-packets.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equidistribution-of-Primitive-Sextic-Torus-Packets-October-5-2026/primitive-sextic-torus-packets.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/015.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "016:The-Abelian-Zilber-Pink-Conjecture-September-24-2026",
      "family_id": "016",
      "discipline": "Number theory",
      "title": "The abelian Zilber\u2013Pink conjecture",
      "pdf_path": "preprints/The-Abelian-Zilber-Pink-Conjecture-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Abelian-Zilber-Pink-Conjecture-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "016:The-E-times-CM-Component-of-Zilber-Pink-for-Curves-in-A2-September-24-2026",
      "family_id": "016",
      "discipline": "Number theory",
      "title": "The E\u00d7CM component of Zilber\u2013Pink for curves in A2",
      "pdf_path": "preprints/The-E-times-CM-Component-of-Zilber-Pink-for-Curves-in-A2-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-E-times-CM-Component-of-Zilber-Pink-for-Curves-in-A2-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "016:Quaternionic-Division-Points-on-Curves-in-the-Siegel-Threefold-September-24-2026",
      "family_id": "016",
      "discipline": "Number theory",
      "title": "Quaternionic division points on curves in the Siegel threefold",
      "pdf_path": "preprints/Quaternionic-Division-Points-on-Curves-in-the-Siegel-Threefold-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Quaternionic-Division-Points-on-Curves-in-the-Siegel-Threefold-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "016:Elliptic-Squares-and-Zilber-Pink-for-Curves-in-A2-September-24-2026",
      "family_id": "016",
      "discipline": "Number theory",
      "title": "Elliptic squares and Zilber\u2013Pink for curves in A2",
      "pdf_path": "preprints/Elliptic-Squares-and-Zilber-Pink-for-Curves-in-A2-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Elliptic-Squares-and-Zilber-Pink-for-Curves-in-A2-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "017:The-irrationality-exponent-of-pi-is-2-September-24-2026",
      "family_id": "017",
      "discipline": "Number theory",
      "title": "The irrationality exponent of pi is 2",
      "pdf_path": "preprints/The-irrationality-exponent-of-pi-is-2-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-irrationality-exponent-of-pi-is-2-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/017.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "018:The-Margulis-Platonov-conjecture-over-global-function-fields-October-5-2026",
      "family_id": "018",
      "discipline": "Number theory",
      "title": "The Margulis\u2013Platonov conjecture over global function fields",
      "pdf_path": "preprints/The-Margulis-Platonov-conjecture-over-global-function-fields-October-5-2026/margulis-platonov-global-function-fields.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Margulis-Platonov-conjecture-over-global-function-fields-October-5-2026/margulis-platonov-global-function-fields.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "018:The-Margulis-Platonov-conjecture-over-number-fields-September-23-2026",
      "family_id": "018",
      "discipline": "Number theory",
      "title": "The Margulis\u2013Platonov conjecture over number fields",
      "pdf_path": "preprints/The-Margulis-Platonov-conjecture-over-number-fields-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Margulis-Platonov-conjecture-over-number-fields-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "019:Etale-covers-with-a-prescribed-exterior-sheet-September-24-2026",
      "family_id": "019",
      "discipline": "Number theory",
      "title": "\u00c9tale covers with a prescribed exterior sheet",
      "pdf_path": "preprints/Etale-covers-with-a-prescribed-exterior-sheet-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Etale-covers-with-a-prescribed-exterior-sheet-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "019:The-p-adic-section-conjecture-October-6-2026",
      "family_id": "019",
      "discipline": "Number theory",
      "title": "The p-adic section conjecture",
      "pdf_path": "preprints/The-p-adic-section-conjecture-October-6-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-p-adic-section-conjecture-October-6-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "020:Squarefree-values-of-quartics-and-power-free-values-of-polynomials-September-24-2026",
      "family_id": "020",
      "discipline": "Number theory",
      "title": "Squarefree values of quartics and power-free values of polynomials",
      "pdf_path": "preprints/Squarefree-values-of-quartics-and-power-free-values-of-polynomials-September-24-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Squarefree-values-of-quartics-and-power-free-values-of-polynomials-September-24-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/020.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "021:A-quadratic-bound-for-Jacobsthals-function-September-25-2026",
      "family_id": "021",
      "discipline": "Number theory",
      "title": "A quadratic bound for Jacobsthal's function",
      "pdf_path": "preprints/A-quadratic-bound-for-Jacobsthals-function-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-quadratic-bound-for-Jacobsthals-function-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/021.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "022:The-weak-inhomogeneous-Duffin-Schaeffer-conjecture-September-25-2026",
      "family_id": "022",
      "discipline": "Number theory",
      "title": "The Weak Inhomogeneous Duffin\u2013Schaeffer Conjecture",
      "pdf_path": "preprints/The-weak-inhomogeneous-Duffin-Schaeffer-conjecture-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-weak-inhomogeneous-Duffin-Schaeffer-conjecture-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "023:An-unconditional-first-moment-for-cubic-Gauss-sums-September-25-2026",
      "family_id": "023",
      "discipline": "Number theory",
      "title": "An unconditional first moment for cubic Gauss sums",
      "pdf_path": "preprints/An-unconditional-first-moment-for-cubic-Gauss-sums-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-unconditional-first-moment-for-cubic-Gauss-sums-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/023.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "024:An-asymptotic-formula-for-the-number-of-totients-September-25-2026",
      "family_id": "024",
      "discipline": "Number theory",
      "title": "An asymptotic formula for the number of totients",
      "pdf_path": "preprints/An-asymptotic-formula-for-the-number-of-totients-September-25-2026/An-asymptotic-formula-for-the-number-of-totients-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-asymptotic-formula-for-the-number-of-totients-September-25-2026/An-asymptotic-formula-for-the-number-of-totients-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/024.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "025:Short-Egyptian-fractions-September-25-2026",
      "family_id": "025",
      "discipline": "Number theory",
      "title": "Short Egyptian fractions",
      "pdf_path": "preprints/Short-Egyptian-fractions-September-25-2026/Short-Egyptian-fractions-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Short-Egyptian-fractions-September-25-2026/Short-Egyptian-fractions-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/025.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "026:Positive-lower-density-of-large-prime-gaps-September-25-2026",
      "family_id": "026",
      "discipline": "Number theory",
      "title": "Positive lower density of large prime gaps",
      "pdf_path": "preprints/Positive-lower-density-of-large-prime-gaps-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Positive-lower-density-of-large-prime-gaps-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/026.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "027:Integral-points-on-character-varieties-of-curves-September-25-2026",
      "family_id": "027",
      "discipline": "Number theory",
      "title": "Integral points on character varieties of curves",
      "pdf_path": "preprints/Integral-points-on-character-varieties-of-curves-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Integral-points-on-character-varieties-of-curves-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/027.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "028:Bounded-Step-Walks-on-Gaussian-Primes-September-26-2026",
      "family_id": "028",
      "discipline": "Number theory",
      "title": "Bounded-Step Walks on Gaussian Primes",
      "pdf_path": "preprints/Bounded-Step-Walks-on-Gaussian-Primes-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Bounded-Step-Walks-on-Gaussian-Primes-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/028.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "029:Primitive-roots-for-every-admissible-integer-base-October-4-2026",
      "family_id": "029",
      "discipline": "Number theory",
      "title": "Primitive roots for every admissible integer base",
      "pdf_path": "preprints/Primitive-roots-for-every-admissible-integer-base-October-4-2026/primitive-roots-all-integer-bases.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Primitive-roots-for-every-admissible-integer-base-October-4-2026/primitive-roots-all-integer-bases.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "029:Simultaneous-primitive-roots-a-conditional-lower-bound-for-prime-bases-October-4-2026",
      "family_id": "029",
      "discipline": "Number theory",
      "title": "Simultaneous primitive roots: a conditional lower bound for prime bases",
      "pdf_path": "preprints/Simultaneous-primitive-roots-a-conditional-lower-bound-for-prime-bases-October-4-2026/simultaneous-primitive-roots-conditional-lower-bound-prime-bases.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Simultaneous-primitive-roots-a-conditional-lower-bound-for-prime-bases-October-4-2026/simultaneous-primitive-roots-conditional-lower-bound-prime-bases.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "030:Modularity-of-elliptic-curves-over-imaginary-quadratic-fields-October-4-2026",
      "family_id": "030",
      "discipline": "Number theory",
      "title": "Modularity of elliptic curves over imaginary quadratic fields",
      "pdf_path": "preprints/Modularity-of-elliptic-curves-over-imaginary-quadratic-fields-October-4-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Modularity-of-elliptic-curves-over-imaginary-quadratic-fields-October-4-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "031:Open-Homomorphisms-of-Global-Solvably-Closed-Galois-Groups-October-5-2026",
      "family_id": "031",
      "discipline": "Number theory",
      "title": "Open Homomorphisms of Global Solvably Closed Galois Groups",
      "pdf_path": "preprints/Open-Homomorphisms-of-Global-Solvably-Closed-Galois-Groups-October-5-2026/open-homomorphisms-solvably-closed-galois-groups.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Open-Homomorphisms-of-Global-Solvably-Closed-Galois-Groups-October-5-2026/open-homomorphisms-solvably-closed-galois-groups.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "032:The-rational-Hodge-conjecture-for-CM-abelian-varieties-October-6-2026",
      "family_id": "032",
      "discipline": "Algebraic and complex geometry",
      "title": "The rational Hodge conjecture for CM abelian varieties",
      "pdf_path": "preprints/The-rational-Hodge-conjecture-for-CM-abelian-varieties-October-6-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-rational-Hodge-conjecture-for-CM-abelian-varieties-October-6-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "032:Algebraic-Kuga-Satake-correspondences-and-Hodge-conjectures-on-a-K3-quadratic-locus-September-30-2026",
      "family_id": "032",
      "discipline": "Algebraic and complex geometry",
      "title": "Algebraic Kuga\u2013Satake correspondences and Hodge conjectures on a K3 quadratic locus",
      "pdf_path": "preprints/Algebraic-Kuga-Satake-correspondences-and-Hodge-conjectures-on-a-K3-quadratic-locus-September-30-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Algebraic-Kuga-Satake-correspondences-and-Hodge-conjectures-on-a-K3-quadratic-locus-September-30-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "032:Weil-classes-and-Hodge-classes-on-abelian-powers-October-6-2026",
      "family_id": "032",
      "discipline": "Algebraic and complex geometry",
      "title": "Weil classes and Hodge classes on abelian powers",
      "pdf_path": "preprints/Weil-classes-and-Hodge-classes-on-abelian-powers-October-6-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weil-classes-and-Hodge-classes-on-abelian-powers-October-6-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "032:Abelian-covers-Gale-correspondences-and-the-Hodge-conjecture-for-powers-October-6-2026",
      "family_id": "032",
      "discipline": "Algebraic and complex geometry",
      "title": "Abelian covers, Gale correspondences, and the Hodge conjecture for powers",
      "pdf_path": "preprints/Abelian-covers-Gale-correspondences-and-the-Hodge-conjecture-for-powers-October-6-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Abelian-covers-Gale-correspondences-and-the-Hodge-conjecture-for-powers-October-6-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "032:A-Conditional-Reduction-for-Algebraic-Kuga-Satake-Correspondences-September-10-2026",
      "family_id": "032",
      "discipline": "Algebraic and complex geometry",
      "title": "A Conditional Reduction for Algebraic Kuga\u2013Satake Correspondences",
      "pdf_path": "preprints/A-Conditional-Reduction-for-Algebraic-Kuga-Satake-Correspondences-September-10-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Conditional-Reduction-for-Algebraic-Kuga-Satake-Correspondences-September-10-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "033:Orbifold-and-logarithmic-Iitaka-subadditivity-September-26-2026",
      "family_id": "033",
      "discipline": "Algebraic and complex geometry",
      "title": "Orbifold and logarithmic Iitaka subadditivity",
      "pdf_path": "preprints/Orbifold-and-logarithmic-Iitaka-subadditivity-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Orbifold-and-logarithmic-Iitaka-subadditivity-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/033.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "033:Logarithmic-Kodaira-dimension-and-whole-fiber-variation-September-26-2026",
      "family_id": "033",
      "discipline": "Algebraic and complex geometry",
      "title": "Logarithmic Kodaira dimension and whole-fiber variation",
      "pdf_path": "preprints/Logarithmic-Kodaira-dimension-and-whole-fiber-variation-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Logarithmic-Kodaira-dimension-and-whole-fiber-variation-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/033.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "033:The-reverse-logarithmic-Kodaira-inequality-and-additivity-September-26-2026",
      "family_id": "033",
      "discipline": "Algebraic and complex geometry",
      "title": "The reverse logarithmic Kodaira inequality and additivity",
      "pdf_path": "preprints/The-reverse-logarithmic-Kodaira-inequality-and-additivity-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-reverse-logarithmic-Kodaira-inequality-and-additivity-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/033.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "033:Projective-Hodge-lines-and-ordinary-Iitaka-subadditivity-September-27-2026",
      "family_id": "033",
      "discipline": "Algebraic and complex geometry",
      "title": "Projective Hodge lines and ordinary Iitaka subadditivity",
      "pdf_path": "preprints/Projective-Hodge-lines-and-ordinary-Iitaka-subadditivity-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Projective-Hodge-lines-and-ordinary-Iitaka-subadditivity-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/033.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "033:B-semiampleness-for-compact-log-smooth-Kahler-fibrations-September-10-2026",
      "family_id": "033",
      "discipline": "Algebraic and complex geometry",
      "title": "B-semiampleness for compact log-smooth K\u00e4hler fibrations",
      "pdf_path": "preprints/B-semiampleness-for-compact-log-smooth-Kahler-fibrations-September-10-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/B-semiampleness-for-compact-log-smooth-Kahler-fibrations-September-10-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/033.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Log-abundance-for-compact-Kahler-spaces-under-logarithmic-Iitaka-subadditivity-October-6-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Log abundance for compact K\u00e4hler spaces under logarithmic Iitaka subadditivity",
      "pdf_path": "preprints/Log-abundance-for-compact-Kahler-spaces-under-logarithmic-Iitaka-subadditivity-October-6-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Log-abundance-for-compact-Kahler-spaces-under-logarithmic-Iitaka-subadditivity-October-6-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Uniform-indices-for-semi-log-canonical-log-Calabi-Yau-pairs-October-5-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Uniform indices for semi-log-canonical log Calabi\u2013Yau pairs",
      "pdf_path": "preprints/Uniform-indices-for-semi-log-canonical-log-Calabi-Yau-pairs-October-5-2026/uniform-slc-index.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-indices-for-semi-log-canonical-log-Calabi-Yau-pairs-October-5-2026/uniform-slc-index.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Conditional-good-minimal-models-for-compact-Kahler-fourfolds-October-6-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Conditional good minimal models for compact K\u00e4hler fourfolds",
      "pdf_path": "preprints/Conditional-good-minimal-models-for-compact-Kahler-fourfolds-October-6-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Conditional-good-minimal-models-for-compact-Kahler-fourfolds-October-6-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Log-abundance-in-characteristic-zero-September-24-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Log abundance in characteristic zero",
      "pdf_path": "preprints/Log-abundance-in-characteristic-zero-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Log-abundance-in-characteristic-zero-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Minimal-metrics-and-interior-injectivity-for-nef-adjoints-September-27-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Minimal metrics and interior injectivity for nef adjoints",
      "pdf_path": "preprints/Minimal-metrics-and-interior-injectivity-for-nef-adjoints-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Minimal-metrics-and-interior-injectivity-for-nef-adjoints-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Fourfold-nonvanishing-by-minimal-metrics-and-moving-jets-September-27-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Fourfold nonvanishing by minimal metrics and moving jets",
      "pdf_path": "preprints/Fourfold-nonvanishing-by-minimal-metrics-and-moving-jets-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Fourfold-nonvanishing-by-minimal-metrics-and-moving-jets-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Lifting-sections-from-the-reduced-support-of-an-adjoint-September-27-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Lifting sections from the reduced support of an adjoint",
      "pdf_path": "preprints/Lifting-sections-from-the-reduced-support-of-an-adjoint-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Lifting-sections-from-the-reduced-support-of-an-adjoint-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Schnell-fiber-spaces-and-good-canonical-models-September-24-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Schnell fiber spaces and good canonical models",
      "pdf_path": "preprints/Schnell-fiber-spaces-and-good-canonical-models-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Schnell-fiber-spaces-and-good-canonical-models-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Uniform-log-Iitaka-fibrations-and-bounded-moduli-denominators-October-4-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Uniform log Iitaka fibrations and bounded moduli denominators",
      "pdf_path": "preprints/Uniform-log-Iitaka-fibrations-and-bounded-moduli-denominators-October-4-2026/uniform-log-iitaka.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-log-Iitaka-fibrations-and-bounded-moduli-denominators-October-4-2026/uniform-log-iitaka.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Uniform-Pluricanonical-Iitaka-Fibrations-October-3-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Uniform Pluricanonical Iitaka Fibrations",
      "pdf_path": "preprints/Uniform-Pluricanonical-Iitaka-Fibrations-October-3-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-Pluricanonical-Iitaka-Fibrations-October-3-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Relative-denominators-and-effective-systems-for-log-Calabi-Yau-fibrations-September-27-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Relative denominators and effective systems for log Calabi-Yau fibrations",
      "pdf_path": "preprints/Relative-denominators-and-effective-systems-for-log-Calabi-Yau-fibrations-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Relative-denominators-and-effective-systems-for-log-Calabi-Yau-fibrations-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Arithmetic-Stein-degree-bounds-for-log-Calabi-Yau-pairs-September-25-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Arithmetic Stein-degree bounds for log Calabi\u2013Yau pairs",
      "pdf_path": "preprints/Arithmetic-Stein-degree-bounds-for-log-Calabi-Yau-pairs-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Arithmetic-Stein-degree-bounds-for-log-Calabi-Yau-pairs-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Uniform-effective-log-Iitaka-fibrations-for-fourfolds-September-26-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Uniform effective log Iitaka fibrations for fourfolds",
      "pdf_path": "preprints/Uniform-effective-log-Iitaka-fibrations-for-fourfolds-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-effective-log-Iitaka-fibrations-for-fourfolds-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "034:Abundance-after-nonvanishing-for-compact-Kahler-fourfolds-September-27-2026",
      "family_id": "034",
      "discipline": "Algebraic and complex geometry",
      "title": "Abundance after nonvanishing for compact K\u00e4hler fourfolds",
      "pdf_path": "preprints/Abundance-after-nonvanishing-for-compact-Kahler-fourfolds-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Abundance-after-nonvanishing-for-compact-Kahler-fourfolds-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "035:Log-abundance-in-numerical-dimension-one-for-threefolds-in-positive-characteristic-October-5-2026",
      "family_id": "035",
      "discipline": "Algebraic and complex geometry",
      "title": "Log abundance in numerical dimension one for threefolds in positive characteristic",
      "pdf_path": "preprints/Log-abundance-in-numerical-dimension-one-for-threefolds-in-positive-characteristic-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Log-abundance-in-numerical-dimension-one-for-threefolds-in-positive-characteristic-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "035:Abundance-in-numerical-dimension-one-for-terminal-threefolds-in-positive-characteristic-September-24-2026",
      "family_id": "035",
      "discipline": "Algebraic and complex geometry",
      "title": "Abundance in numerical dimension one for terminal threefolds in positive characteristic",
      "pdf_path": "preprints/Abundance-in-numerical-dimension-one-for-terminal-threefolds-in-positive-characteristic-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Abundance-in-numerical-dimension-one-for-terminal-threefolds-in-positive-characteristic-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "036:Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-6-2026",
      "family_id": "036",
      "discipline": "Algebraic and complex geometry",
      "title": "Numerical semiampleness of nef adjoint classes on compact K\u00e4hler manifolds",
      "pdf_path": "preprints/Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-6-2026/numerical-generalized-abundance.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-6-2026/numerical-generalized-abundance.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "036:Numerical-Semiampleness-of-Nef-Adjoint-Divisors-October-3-2026",
      "family_id": "036",
      "discipline": "Algebraic and complex geometry",
      "title": "Numerical Semiampleness of Nef Adjoint Divisors",
      "pdf_path": "preprints/Numerical-Semiampleness-of-Nef-Adjoint-Divisors-October-3-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Numerical-Semiampleness-of-Nef-Adjoint-Divisors-October-3-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "036:Minimal-models-and-Mori-fibre-spaces-for-generalized-log-canonical-Q-pairs-September-24-2026",
      "family_id": "036",
      "discipline": "Algebraic and complex geometry",
      "title": "Minimal models and Mori fibre spaces for generalized log canonical Q-pairs",
      "pdf_path": "preprints/Minimal-models-and-Mori-fibre-spaces-for-generalized-log-canonical-Q-pairs-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Minimal-models-and-Mori-fibre-spaces-for-generalized-log-canonical-Q-pairs-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "036:Minimal-models-in-numerical-dimension-one-September-24-2026",
      "family_id": "036",
      "discipline": "Algebraic and complex geometry",
      "title": "Minimal models in numerical dimension one",
      "pdf_path": "preprints/Minimal-models-in-numerical-dimension-one-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Minimal-models-in-numerical-dimension-one-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "037:The-ordinary-double-point-gap-in-every-dimension-September-24-2026",
      "family_id": "037",
      "discipline": "Algebraic and complex geometry",
      "title": "The ordinary-double-point gap in every dimension",
      "pdf_path": "preprints/The-ordinary-double-point-gap-in-every-dimension-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-ordinary-double-point-gap-in-every-dimension-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "037:The-normalized-volume-gap-in-dimension-four-September-24-2026",
      "family_id": "037",
      "discipline": "Algebraic and complex geometry",
      "title": "The normalized-volume gap in dimension four",
      "pdf_path": "preprints/The-normalized-volume-gap-in-dimension-four-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-normalized-volume-gap-in-dimension-four-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "038:Fujitas-freeness-conjecture-September-23-2026",
      "family_id": "038",
      "discipline": "Algebraic and complex geometry",
      "title": "Fujita's freeness conjecture",
      "pdf_path": "preprints/Fujitas-freeness-conjecture-September-23-2026/Fujitas-freeness-conjecture-September-23-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Fujitas-freeness-conjecture-September-23-2026/Fujitas-freeness-conjecture-September-23-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "039:Nagatas-Conjecture-for-Plane-Curves-September-23-2026",
      "family_id": "039",
      "discipline": "Algebraic and complex geometry",
      "title": "Nagata's conjecture for plane curves",
      "pdf_path": "preprints/Nagatas-Conjecture-for-Plane-Curves-September-23-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nagatas-Conjecture-for-Plane-Curves-September-23-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/039.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "039:Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026",
      "family_id": "039",
      "discipline": "Algebraic and complex geometry",
      "title": "Maximal Seshadri constants on arbitrary polarized surfaces",
      "pdf_path": "preprints/Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/039.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "039:Maximal-Multipoint-Seshadri-Constants-in-Higher-Dimensions-October-5-2026",
      "family_id": "039",
      "discipline": "Algebraic and complex geometry",
      "title": "Maximal Multipoint Seshadri Constants in Higher Dimensions",
      "pdf_path": "preprints/Maximal-Multipoint-Seshadri-Constants-in-Higher-Dimensions-October-5-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Maximal-Multipoint-Seshadri-Constants-in-Higher-Dimensions-October-5-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/039.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "039:Maximal-multipoint-Seshadri-constants-in-positive-characteristic-October-5-2026",
      "family_id": "039",
      "discipline": "Algebraic and complex geometry",
      "title": "Maximal multipoint Seshadri constants in positive characteristic",
      "pdf_path": "preprints/Maximal-multipoint-Seshadri-constants-in-positive-characteristic-October-5-2026/seshadri-positive-characteristic.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Maximal-multipoint-Seshadri-constants-in-positive-characteristic-October-5-2026/seshadri-positive-characteristic.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/039.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "040:Blochs-Conjecture-for-Surfaces-with-pg-equals-q-equals-0-September-24-2026",
      "family_id": "040",
      "discipline": "Algebraic and complex geometry",
      "title": "Bloch\u2019s conjecture for surfaces with p_g=0",
      "pdf_path": "preprints/Blochs-Conjecture-for-Surfaces-with-pg-equals-q-equals-0-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Blochs-Conjecture-for-Surfaces-with-pg-equals-q-equals-0-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "041:Projective-Space-Bases-of-Lagrangian-Fibrations-September-23-2026",
      "family_id": "041",
      "discipline": "Algebraic and complex geometry",
      "title": "Projective-space bases of Lagrangian fibrations",
      "pdf_path": "preprints/Projective-Space-Bases-of-Lagrangian-Fibrations-September-23-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Projective-Space-Bases-of-Lagrangian-Fibrations-September-23-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "041:The-Strong-Hyperkahler-SYZ-Conjecture-September-23-2026",
      "family_id": "041",
      "discipline": "Algebraic and complex geometry",
      "title": "The strong hyperk\u00e4hler SYZ conjecture",
      "pdf_path": "preprints/The-Strong-Hyperkahler-SYZ-Conjecture-September-23-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Strong-Hyperkahler-SYZ-Conjecture-September-23-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "042:Every-complex-K3-surface-is-Oka-September-23-2026",
      "family_id": "042",
      "discipline": "Algebraic and complex geometry",
      "title": "Every complex K3 surface is Oka",
      "pdf_path": "preprints/Every-complex-K3-surface-is-Oka-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Every-complex-K3-surface-is-Oka-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "043:P-equals-W-in-composite-rank-for-fixed-determinant-September-24-2026",
      "family_id": "043",
      "discipline": "Algebraic and complex geometry",
      "title": "P=W in composite rank for fixed determinant",
      "pdf_path": "preprints/P-equals-W-in-composite-rank-for-fixed-determinant-September-24-2026/P-equals-W-in-composite-rank-for-fixed-determinant-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/P-equals-W-in-composite-rank-for-fixed-determinant-September-24-2026/P-equals-W-in-composite-rank-for-fixed-determinant-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "044:The-equivariant-cohomological-Hikita-conjecture-for-arbitrary-quivers-September-24-2026",
      "family_id": "044",
      "discipline": "Algebraic and complex geometry",
      "title": "The equivariant cohomological Hikita conjecture for arbitrary quivers",
      "pdf_path": "preprints/The-equivariant-cohomological-Hikita-conjecture-for-arbitrary-quivers-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-equivariant-cohomological-Hikita-conjecture-for-arbitrary-quivers-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "046:A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026",
      "family_id": "046",
      "discipline": "Algebraic and complex geometry",
      "title": "A projective fourfold with large fundamental group and non-Stein universal cover",
      "pdf_path": "preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026/large-fundamental-group-non-stein.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026/large-fundamental-group-non-stein.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "046:A-surface-counterexample-to-Shafarevich-holomorphic-convexity-September-23-2026",
      "family_id": "046",
      "discipline": "Algebraic and complex geometry",
      "title": "A surface counterexample to Shafarevich holomorphic convexity",
      "pdf_path": "preprints/A-surface-counterexample-to-Shafarevich-holomorphic-convexity-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-surface-counterexample-to-Shafarevich-holomorphic-convexity-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "047:An-explicit-failure-of-complex-affine-space-cancellation-September-23-2026",
      "family_id": "047",
      "discipline": "Algebraic and complex geometry",
      "title": "An explicit failure of complex affine-space cancellation",
      "pdf_path": "preprints/An-explicit-failure-of-complex-affine-space-cancellation-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-explicit-failure-of-complex-affine-space-cancellation-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/047.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "048:A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026",
      "family_id": "048",
      "discipline": "Algebraic and complex geometry",
      "title": "A singular normal affine surface with free tangent sheaf",
      "pdf_path": "preprints/A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "049:A-stable-coordinate-that-is-not-a-coordinate-in-four-variables-October-5-2026",
      "family_id": "049",
      "discipline": "Algebraic and complex geometry",
      "title": "A stable coordinate that is not a coordinate in four variables",
      "pdf_path": "preprints/A-stable-coordinate-that-is-not-a-coordinate-in-four-variables-October-5-2026/stable-coordinate-four-variables.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-stable-coordinate-that-is-not-a-coordinate-in-four-variables-October-5-2026/stable-coordinate-four-variables.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/049.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "049:An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre-September-24-2026",
      "family_id": "049",
      "discipline": "Algebraic and complex geometry",
      "title": "An explicit noncoordinate polynomial with affine three-space zero fibre",
      "pdf_path": "preprints/An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/049.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "050:ample-rank-two-bundles-on-the-quadric-surface-without-griffiths-positive-metrics-September-24-2026",
      "family_id": "050",
      "discipline": "Algebraic and complex geometry",
      "title": "Ample rank-two bundles on the quadric surface without Griffiths-positive metrics",
      "pdf_path": "preprints/ample-rank-two-bundles-on-the-quadric-surface-without-griffiths-positive-metrics-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/ample-rank-two-bundles-on-the-quadric-surface-without-griffiths-positive-metrics-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/050.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "051:Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026",
      "family_id": "051",
      "discipline": "Algebraic and complex geometry",
      "title": "Canonical ampleness of compact hyperbolic K\u00e4hler manifolds",
      "pdf_path": "preprints/Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026/canonical-ampleness.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026/canonical-ampleness.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "052:Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026",
      "family_id": "052",
      "discipline": "Algebraic and complex geometry",
      "title": "Universal-cover splitting for compact K\u00e4hler manifolds",
      "pdf_path": "preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/052.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "052:Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds-September-23-2026",
      "family_id": "052",
      "discipline": "Algebraic and complex geometry",
      "title": "Integrability of split tangent bundles on rationally connected manifolds",
      "pdf_path": "preprints/Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds-September-23-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds-September-23-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/052.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "053:A-high-arity-counterexample-to-Pixton-completeness-in-Chow-September-24-2026",
      "family_id": "053",
      "discipline": "Algebraic and complex geometry",
      "title": "A high-arity counterexample to Pixton completeness in Chow",
      "pdf_path": "preprints/A-high-arity-counterexample-to-Pixton-completeness-in-Chow-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-high-arity-counterexample-to-Pixton-completeness-in-Chow-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "054:Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026",
      "family_id": "054",
      "discipline": "Algebraic and complex geometry",
      "title": "Irrational cubic fourfolds with geometric K3 categories",
      "pdf_path": "preprints/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "055:A-Gepner-stability-condition-on-every-smooth-quintic-threefold-September-24-2026",
      "family_id": "055",
      "discipline": "Algebraic and complex geometry",
      "title": "A Gepner stability condition on every smooth quintic threefold",
      "pdf_path": "preprints/A-Gepner-stability-condition-on-every-smooth-quintic-threefold-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Gepner-stability-condition-on-every-smooth-quintic-threefold-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "055:Prescribed-large-volume-charges-on-threefolds-with-trivial-canonical-bundle-September-24-2026",
      "family_id": "055",
      "discipline": "Algebraic and complex geometry",
      "title": "Prescribed large-volume charges on threefolds with trivial canonical bundle",
      "pdf_path": "preprints/Prescribed-large-volume-charges-on-threefolds-with-trivial-canonical-bundle-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Prescribed-large-volume-charges-on-threefolds-with-trivial-canonical-bundle-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "056:Termination-of-generalized-log-canonical-flips-on-compact-Kahler-fourfolds-October-7-2026",
      "family_id": "056",
      "discipline": "Algebraic and complex geometry",
      "title": "Termination of generalized log canonical flips on compact K\u00e4hler fourfolds",
      "pdf_path": "preprints/Termination-of-generalized-log-canonical-flips-on-compact-Kahler-fourfolds-October-7-2026/termination-generalized-lc-kahler-fourfolds.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Termination-of-generalized-log-canonical-flips-on-compact-Kahler-fourfolds-October-7-2026/termination-generalized-lc-kahler-fourfolds.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "056:Termination-of-generalized-canonical-flips-on-compact-Kahler-fourfolds-October-6-2026",
      "family_id": "056",
      "discipline": "Algebraic and complex geometry",
      "title": "Termination of generalized-canonical flips on compact K\u00e4hler fourfolds",
      "pdf_path": "preprints/Termination-of-generalized-canonical-flips-on-compact-Kahler-fourfolds-October-6-2026/termination-generalized-terminal-flips-compact-kahler-fourfolds.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Termination-of-generalized-canonical-flips-on-compact-Kahler-fourfolds-October-6-2026/termination-generalized-terminal-flips-compact-kahler-fourfolds.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "056:Termination-for-projective-log-canonical-fourfolds-with-rational-boundary-September-24-2026",
      "family_id": "056",
      "discipline": "Algebraic and complex geometry",
      "title": "Termination for projective log canonical fourfolds with rational boundary",
      "pdf_path": "preprints/Termination-for-projective-log-canonical-fourfolds-with-rational-boundary-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Termination-for-projective-log-canonical-fourfolds-with-rational-boundary-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "056:Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026",
      "family_id": "056",
      "discipline": "Algebraic and complex geometry",
      "title": "Finite ordinary minimal model programs on compact K\u00e4hler fourfolds",
      "pdf_path": "preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "056:Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-September-24-2026",
      "family_id": "056",
      "discipline": "Algebraic and complex geometry",
      "title": "Finite ordinary minimal model programs on compact K\u00e4hler fourfolds",
      "pdf_path": "preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "057:The-abelianity-conjecture-for-special-compact-Kahler-manifolds-September-23-2026",
      "family_id": "057",
      "discipline": "Algebraic and complex geometry",
      "title": "The abelianity conjecture for special compact K\u00e4hler manifolds",
      "pdf_path": "preprints/The-abelianity-conjecture-for-special-compact-Kahler-manifolds-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-abelianity-conjecture-for-special-compact-Kahler-manifolds-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "057:Two-step-monodromy-of-special-quasi-projective-varieties-September-24-2026",
      "family_id": "057",
      "discipline": "Algebraic and complex geometry",
      "title": "Two-step monodromy of special quasi-projective varieties",
      "pdf_path": "preprints/Two-step-monodromy-of-special-quasi-projective-varieties-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Two-step-monodromy-of-special-quasi-projective-varieties-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "057:A-conditional-abelianity-theorem-for-special-fourfold-pairs-with-a-half-weight-divisor-October-5-2026",
      "family_id": "057",
      "discipline": "Algebraic and complex geometry",
      "title": "A conditional abelianity theorem for special fourfold pairs with a half-weight divisor",
      "pdf_path": "preprints/A-conditional-abelianity-theorem-for-special-fourfold-pairs-with-a-half-weight-divisor-October-5-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-conditional-abelianity-theorem-for-special-fourfold-pairs-with-a-half-weight-divisor-October-5-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "058:Semialgebraic-universal-covers-of-normal-projective-varieties-September-24-2026",
      "family_id": "058",
      "discipline": "Algebraic and complex geometry",
      "title": "Semialgebraic universal covers of normal projective varieties",
      "pdf_path": "preprints/Semialgebraic-universal-covers-of-normal-projective-varieties-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Semialgebraic-universal-covers-of-normal-projective-varieties-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/058.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "058:Symmetry-of-semialgebraic-bounded-domains-with-compact-quotient-September-24-2026",
      "family_id": "058",
      "discipline": "Algebraic and complex geometry",
      "title": "Symmetry of semialgebraic bounded domains with compact quotient",
      "pdf_path": "preprints/Symmetry-of-semialgebraic-bounded-domains-with-compact-quotient-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Symmetry-of-semialgebraic-bounded-domains-with-compact-quotient-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/058.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "059:Ambiently-homeomorphic-isolated-hypersurfaces-of-multiplicities-two-and-three-September-24-2026",
      "family_id": "059",
      "discipline": "Algebraic and complex geometry",
      "title": "Ambiently homeomorphic isolated hypersurfaces of multiplicities two and three",
      "pdf_path": "preprints/Ambiently-homeomorphic-isolated-hypersurfaces-of-multiplicities-two-and-three-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Ambiently-homeomorphic-isolated-hypersurfaces-of-multiplicities-two-and-three-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "059:Ambiently-homeomorphic-isolated-hypersurface-germs-in-C4-with-multiplicities-four-and-five-September-27-2026",
      "family_id": "059",
      "discipline": "Algebraic and complex geometry",
      "title": "Ambiently homeomorphic isolated hypersurface germs in \u2102\u2074 with multiplicities four and five",
      "pdf_path": "preprints/Ambiently-homeomorphic-isolated-hypersurface-germs-in-C4-with-multiplicities-four-and-five-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Ambiently-homeomorphic-isolated-hypersurface-germs-in-C4-with-multiplicities-four-and-five-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "060:Global-Spherical-Shells-on-Minimal-Surfaces-of-Class-VII-September-24-2026",
      "family_id": "060",
      "discipline": "Algebraic and complex geometry",
      "title": "Global Spherical Shells on Minimal Surfaces of Class VII",
      "pdf_path": "preprints/Global-Spherical-Shells-on-Minimal-Surfaces-of-Class-VII-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Spherical-Shells-on-Minimal-Surfaces-of-Class-VII-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "062:Contact-Fano-manifolds-and-the-LeBrun-Salamon-conjecture-September-23-2026",
      "family_id": "062",
      "discipline": "Algebraic and complex geometry",
      "title": "Contact Fano manifolds and the LeBrun\u2013Salamon conjecture",
      "pdf_path": "preprints/Contact-Fano-manifolds-and-the-LeBrun-Salamon-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Contact-Fano-manifolds-and-the-LeBrun-Salamon-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "063:The-Generalized-Mukai-Conjecture-September-24-2026",
      "family_id": "063",
      "discipline": "Algebraic and complex geometry",
      "title": "The generalized Mukai conjecture",
      "pdf_path": "preprints/The-Generalized-Mukai-Conjecture-September-24-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Generalized-Mukai-Conjecture-September-24-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "064:Topological-triviality-of-mu-constant-families-of-surface-singularities-September-24-2026",
      "family_id": "064",
      "discipline": "Algebraic and complex geometry",
      "title": "Topological triviality of mu-constant families of surface singularities",
      "pdf_path": "preprints/Topological-triviality-of-mu-constant-families-of-surface-singularities-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Topological-triviality-of-mu-constant-families-of-surface-singularities-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "065:Virasoro-Constraints-under-Projectivization-October-5-2026",
      "family_id": "065",
      "discipline": "Algebraic and complex geometry",
      "title": "Virasoro Constraints under Projectivization",
      "pdf_path": "preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/virasoro-constraints-under-projectivization.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/virasoro-constraints-under-projectivization.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/build/sections/01-introduction.tex",
          "extent": "selected sections as documented in family addendum",
          "note": "The October 5 introduction transfers all-genus ordinary Virasoro constraints from a smooth connected complex projective base to projectivization of an arbitrary algebraic vector bundle of rank at least two. The bundle need not split or be positive; the base need not have semisimple quantum cohomology. Actual integral curve classes, odd insertions and the first Hodge grading are specified. The premise that the base satisfies the constraints remains necessary. Coefficientwise finiteness and ancestor bounds in the proof do not automatically give a triangular, initialized or efficient numerical recurrence engine. The earlier complete-intersection manuscript and proof details remain queued. There is no family formal-scope document.",
          "sha256": "382baec624aa0ea2b408e030fd9d6358ce97f635c5c178b6c2d0e95dc5a8f4a0"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "065:Virasoro-Constraints-for-Projective-Complete-Intersections-September-24-2026",
      "family_id": "065",
      "discipline": "Algebraic and complex geometry",
      "title": "Virasoro Constraints for Projective Complete Intersections",
      "pdf_path": "preprints/Virasoro-Constraints-for-Projective-Complete-Intersections-September-24-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Virasoro-Constraints-for-Projective-Complete-Intersections-September-24-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "066:Bounded-klt-complements-for-Fano-contractions-September-25-2026",
      "family_id": "066",
      "discipline": "Algebraic and complex geometry",
      "title": "Bounded klt complements for Fano contractions",
      "pdf_path": "preprints/Bounded-klt-complements-for-Fano-contractions-September-25-2026/Bounded-klt-complements-for-Fano-contractions-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Bounded-klt-complements-for-Fano-contractions-September-25-2026/Bounded-klt-complements-for-Fano-contractions-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/066.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "066:Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026",
      "family_id": "066",
      "discipline": "Algebraic and complex geometry",
      "title": "Uniform Cartier sections for Fano type contractions",
      "pdf_path": "preprints/Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026/Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026/Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/066.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "067:The-Campana-Peternell-conjecture-in-dimension-six-September-25-2026",
      "family_id": "067",
      "discipline": "Algebraic and complex geometry",
      "title": "The Campana\u2013Peternell conjecture in dimension six",
      "pdf_path": "preprints/The-Campana-Peternell-conjecture-in-dimension-six-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Campana-Peternell-conjecture-in-dimension-six-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "068:Anticanonical-nonvanishing-from-smooth-semipositivity-September-26-2026",
      "family_id": "068",
      "discipline": "Algebraic and complex geometry",
      "title": "Anticanonical nonvanishing from smooth semipositivity",
      "pdf_path": "preprints/Anticanonical-nonvanishing-from-smooth-semipositivity-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Anticanonical-nonvanishing-from-smooth-semipositivity-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "068:Invariant-anticanonical-indices-and-conversion-of-twisted-differentials-September-26-2026",
      "family_id": "068",
      "discipline": "Algebraic and complex geometry",
      "title": "Invariant anticanonical indices and conversion of twisted differentials",
      "pdf_path": "preprints/Invariant-anticanonical-indices-and-conversion-of-twisted-differentials-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Invariant-anticanonical-indices-and-conversion-of-twisted-differentials-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "068:Bounded-anticanonical-metrics-on-klt-pairs-and-torus-quotients-September-26-2026",
      "family_id": "068",
      "discipline": "Algebraic and complex geometry",
      "title": "Bounded anticanonical metrics on klt pairs and torus quotients",
      "pdf_path": "preprints/Bounded-anticanonical-metrics-on-klt-pairs-and-torus-quotients-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Bounded-anticanonical-metrics-on-klt-pairs-and-torus-quotients-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "068:Cohomological-transfer-and-equivariant-anticanonical-sections-September-26-2026",
      "family_id": "068",
      "discipline": "Algebraic and complex geometry",
      "title": "Cohomological transfer and equivariant anticanonical sections",
      "pdf_path": "preprints/Cohomological-transfer-and-equivariant-anticanonical-sections-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Cohomological-transfer-and-equivariant-anticanonical-sections-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "068:Metric-descent-and-rank-preserving-contractions-September-26-2026",
      "family_id": "068",
      "discipline": "Algebraic and complex geometry",
      "title": "Metric descent and rank-preserving contractions",
      "pdf_path": "preprints/Metric-descent-and-rank-preserving-contractions-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Metric-descent-and-rank-preserving-contractions-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "068:Integrable-metrics-and-effectivity-with-controlled-boundary-September-26-2026",
      "family_id": "068",
      "discipline": "Algebraic and complex geometry",
      "title": "Integrable metrics and effectivity with controlled boundary",
      "pdf_path": "preprints/Integrable-metrics-and-effectivity-with-controlled-boundary-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Integrable-metrics-and-effectivity-with-controlled-boundary-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "068:Exact-orders-and-invariant-anticanonical-linear-systems-September-26-2026",
      "family_id": "068",
      "discipline": "Algebraic and complex geometry",
      "title": "Exact orders and invariant anticanonical linear systems",
      "pdf_path": "preprints/Exact-orders-and-invariant-anticanonical-linear-systems-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-orders-and-invariant-anticanonical-linear-systems-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "069:Global-quantum-geometric-Langlands-at-irrational-level-October-4-2026",
      "family_id": "069",
      "discipline": "Algebraic and complex geometry",
      "title": "Global quantum geometric Langlands at irrational level",
      "pdf_path": "preprints/Global-quantum-geometric-Langlands-at-irrational-level-October-4-2026/quantum-langlands.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-quantum-geometric-Langlands-at-irrational-level-October-4-2026/quantum-langlands.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "071:Removable-Boundaries-and-Rigidity-of-Circle-Domains-September-23-2026",
      "family_id": "071",
      "discipline": "Real and complex analysis",
      "title": "Removable Boundaries and Rigidity of Circle Domains",
      "pdf_path": "preprints/Removable-Boundaries-and-Rigidity-of-Circle-Domains-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Removable-Boundaries-and-Rigidity-of-Circle-Domains-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/071.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "071:Koebes-Circle-Domain-Conjecture-September-23-2026",
      "family_id": "071",
      "discipline": "Real and complex analysis",
      "title": "Koebe's Circle-Domain Conjecture",
      "pdf_path": "preprints/Koebes-Circle-Domain-Conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Koebes-Circle-Domain-Conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/071.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "072:Brennans-conjecture-and-sharp-inverse-square-integral-means-September-24-2026",
      "family_id": "072",
      "discipline": "Real and complex analysis",
      "title": "Brennan's conjecture and sharp inverse-square integral means",
      "pdf_path": "preprints/Brennans-conjecture-and-sharp-inverse-square-integral-means-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Brennans-conjecture-and-sharp-inverse-square-integral-means-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/072.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "072:A-strict-inverse-first-power-bound-for-univalent-functions-September-24-2026",
      "family_id": "072",
      "discipline": "Real and complex analysis",
      "title": "A strict inverse-first-power bound for univalent functions",
      "pdf_path": "preprints/A-strict-inverse-first-power-bound-for-univalent-functions-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-strict-inverse-first-power-bound-for-univalent-functions-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/072.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "073:The-Falconer-distance-conjecture-in-all-dimensions-September-23-2026",
      "family_id": "073",
      "discipline": "Real and complex analysis",
      "title": "The Falconer distance conjecture in all dimensions",
      "pdf_path": "preprints/The-Falconer-distance-conjecture-in-all-dimensions-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Falconer-distance-conjecture-in-all-dimensions-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/073.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "074:The-Kakeya-maximal-conjecture-in-three-dimensions-September-23-2026",
      "family_id": "074",
      "discipline": "Real and complex analysis",
      "title": "The Kakeya maximal conjecture in three dimensions",
      "pdf_path": "preprints/The-Kakeya-maximal-conjecture-in-three-dimensions-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Kakeya-maximal-conjecture-in-three-dimensions-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "074:Every-four-dimensional-Kakeya-set-has-full-Hausdorff-dimension-September-24-2026",
      "family_id": "074",
      "discipline": "Real and complex analysis",
      "title": "Every four-dimensional Kakeya set has full Hausdorff dimension",
      "pdf_path": "preprints/Every-four-dimensional-Kakeya-set-has-full-Hausdorff-dimension-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Every-four-dimensional-Kakeya-set-has-full-Hausdorff-dimension-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "075:Almost-everywhere-Fourier-convergence-in-L-log-L-September-23-2026",
      "family_id": "075",
      "discipline": "Real and complex analysis",
      "title": "Almost-everywhere Fourier convergence in L log L",
      "pdf_path": "preprints/Almost-everywhere-Fourier-convergence-in-L-log-L-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Almost-everywhere-Fourier-convergence-in-L-log-L-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/075.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "076:Ultraflat-real-Littlewood-polynomials-October-5-2026",
      "family_id": "076",
      "discipline": "Real and complex analysis",
      "title": "Ultraflat real Littlewood polynomials",
      "pdf_path": "preprints/Ultraflat-real-Littlewood-polynomials-October-5-2026/ultraflat-real-littlewood-polynomials.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Ultraflat-real-Littlewood-polynomials-October-5-2026/ultraflat-real-littlewood-polynomials.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/076.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "076:Nearly-minimal-maxima-and-positive-minima-of-Littlewood-polynomials-October-5-2026",
      "family_id": "076",
      "discipline": "Real and complex analysis",
      "title": "Nearly minimal maxima and positive minima of Littlewood polynomials",
      "pdf_path": "preprints/Nearly-minimal-maxima-and-positive-minima-of-Littlewood-polynomials-October-5-2026/littlewood-lower-envelope.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nearly-minimal-maxima-and-positive-minima-of-Littlewood-polynomials-October-5-2026/littlewood-lower-envelope.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/076.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "076:Asymptotically-minimal-maxima-of-real-Littlewood-polynomials-September-23-2026",
      "family_id": "076",
      "discipline": "Real and complex analysis",
      "title": "Asymptotically minimal maxima of real Littlewood polynomials",
      "pdf_path": "preprints/Asymptotically-minimal-maxima-of-real-Littlewood-polynomials-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Asymptotically-minimal-maxima-of-real-Littlewood-polynomials-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/076.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "077:Elliptic-capacity-propagation-and-Fourier-restriction-to-the-sphere-September-24-2026",
      "family_id": "077",
      "discipline": "Real and complex analysis",
      "title": "Elliptic capacity propagation and Fourier restriction to the sphere",
      "pdf_path": "preprints/Elliptic-capacity-propagation-and-Fourier-restriction-to-the-sphere-September-24-2026/Elliptic-capacity-propagation-and-Fourier-restriction-to-the-sphere-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Elliptic-capacity-propagation-and-Fourier-restriction-to-the-sphere-September-24-2026/Elliptic-capacity-propagation-and-Fourier-restriction-to-the-sphere-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "077:Diagonal-Fourier-extension-for-positively-curved-surfaces-in-three-dimensions-September-24-2026",
      "family_id": "077",
      "discipline": "Real and complex analysis",
      "title": "Diagonal Fourier extension for positively curved surfaces in three dimensions",
      "pdf_path": "preprints/Diagonal-Fourier-extension-for-positively-curved-surfaces-in-three-dimensions-September-24-2026/Diagonal-Fourier-extension-for-positively-curved-surfaces-in-three-dimensions-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Diagonal-Fourier-extension-for-positively-curved-surfaces-in-three-dimensions-September-24-2026/Diagonal-Fourier-extension-for-positively-curved-surfaces-in-three-dimensions-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "078:Bochner-Riesz-Multipliers-in-Three-Dimensions-September-24-2026",
      "family_id": "078",
      "discipline": "Real and complex analysis",
      "title": "Bochner\u2013Riesz multipliers in three dimensions",
      "pdf_path": "preprints/Bochner-Riesz-Multipliers-in-Three-Dimensions-September-24-2026/Bochner-Riesz-Multipliers-in-Three-Dimensions-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Bochner-Riesz-Multipliers-in-Three-Dimensions-September-24-2026/Bochner-Riesz-Multipliers-in-Three-Dimensions-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "079:Critical-local-smoothing-for-the-three-dimensional-wave-equation-September-24-2026",
      "family_id": "079",
      "discipline": "Real and complex analysis",
      "title": "Critical local smoothing for the three-dimensional wave equation",
      "pdf_path": "preprints/Critical-local-smoothing-for-the-three-dimensional-wave-equation-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Critical-local-smoothing-for-the-three-dimensional-wave-equation-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "080:Endpoint-convergence-for-the-planar-Schrodinger-equation-September-24-2026",
      "family_id": "080",
      "discipline": "Real and complex analysis",
      "title": "Endpoint convergence for the planar Schrodinger equation",
      "pdf_path": "preprints/Endpoint-convergence-for-the-planar-Schrodinger-equation-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Endpoint-convergence-for-the-planar-Schrodinger-equation-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "080:Endpoint-pointwise-convergence-for-the-Schrodinger-equation-in-higher-dimensions-September-24-2026",
      "family_id": "080",
      "discipline": "Real and complex analysis",
      "title": "Endpoint pointwise convergence for the Schrodinger equation in higher dimensions",
      "pdf_path": "preprints/Endpoint-pointwise-convergence-for-the-Schrodinger-equation-in-higher-dimensions-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Endpoint-pointwise-convergence-for-the-Schrodinger-equation-in-higher-dimensions-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "081:Riesz-transforms-and-uniform-rectifiability-in-higher-codimension-September-24-2026",
      "family_id": "081",
      "discipline": "Real and complex analysis",
      "title": "Riesz transforms and uniform rectifiability in higher codimension",
      "pdf_path": "preprints/Riesz-transforms-and-uniform-rectifiability-in-higher-codimension-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Riesz-transforms-and-uniform-rectifiability-in-higher-codimension-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/081.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "082:Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026",
      "family_id": "082",
      "discipline": "Real and complex analysis",
      "title": "Annular variation of the triangular Hilbert transform at the symmetric point",
      "pdf_path": "preprints/Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026/annular-variation.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026/annular-variation.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/082.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "082:An-L3-bound-for-the-dyadic-triangular-Hilbert-form-October-5-2026",
      "family_id": "082",
      "discipline": "Real and complex analysis",
      "title": "An L\u00b3 bound for the dyadic triangular Hilbert form",
      "pdf_path": "preprints/An-L3-bound-for-the-dyadic-triangular-Hilbert-form-October-5-2026/dyadic-triangular-hilbert.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-L3-bound-for-the-dyadic-triangular-Hilbert-form-October-5-2026/dyadic-triangular-hilbert.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/082.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "082:The-maximal-triangular-Hilbert-transform-at-the-symmetric-point-September-24-2026",
      "family_id": "082",
      "discipline": "Real and complex analysis",
      "title": "The maximal triangular Hilbert transform at the symmetric point",
      "pdf_path": "preprints/The-maximal-triangular-Hilbert-transform-at-the-symmetric-point-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-maximal-triangular-Hilbert-transform-at-the-symmetric-point-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/082.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "083:A-uniform-Hilbert-transform-estimate-for-Lipschitz-directions-September-25-2026",
      "family_id": "083",
      "discipline": "Real and complex analysis",
      "title": "A uniform Hilbert transform estimate for Lipschitz directions",
      "pdf_path": "preprints/A-uniform-Hilbert-transform-estimate-for-Lipschitz-directions-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-uniform-Hilbert-transform-estimate-for-Lipschitz-directions-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/083.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "084:The-geometric-case-of-the-Erdos-similarity-conjecture-October-5-2026",
      "family_id": "084",
      "discipline": "Real and complex analysis",
      "title": "The geometric case of the Erd\u0151s similarity conjecture",
      "pdf_path": "preprints/The-geometric-case-of-the-Erdos-similarity-conjecture-October-5-2026/geometric-erdos-similarity.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-geometric-case-of-the-Erdos-similarity-conjecture-October-5-2026/geometric-erdos-similarity.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/084.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "084:The-dyadic-case-of-the-Erdos-similarity-conjecture-September-25-2026",
      "family_id": "084",
      "discipline": "Real and complex analysis",
      "title": "The dyadic case of the Erd\u0151s similarity conjecture",
      "pdf_path": "preprints/The-dyadic-case-of-the-Erdos-similarity-conjecture-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-dyadic-case-of-the-Erdos-similarity-conjecture-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/084.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "085:An-Endpoint-Gradient-Bound-for-the-Centered-Disk-Maximal-Operator-September-26-2026",
      "family_id": "085",
      "discipline": "Real and complex analysis",
      "title": "An Endpoint Gradient Bound for the Centered Disk Maximal Operator",
      "pdf_path": "preprints/An-Endpoint-Gradient-Bound-for-the-Centered-Disk-Maximal-Operator-September-26-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-Endpoint-Gradient-Bound-for-the-Centered-Disk-Maximal-Operator-September-26-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/085.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "086:An-L3-bound-for-the-trilinear-Hilbert-transform-October-5-2026",
      "family_id": "086",
      "discipline": "Real and complex analysis",
      "title": "An <i>L</i><sup>3</sup> bound for the trilinear Hilbert transform",
      "pdf_path": "preprints/An-L3-bound-for-the-trilinear-Hilbert-transform-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-L3-bound-for-the-trilinear-Hilbert-transform-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "087:The-symmetric-Mahler-conjecture-and-its-equality-cases-September-22-2026",
      "family_id": "087",
      "discipline": "Convex and metric geometry",
      "title": "The symmetric Mahler conjecture and its equality cases",
      "pdf_path": "preprints/The-symmetric-Mahler-conjecture-and-its-equality-cases-September-22-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-symmetric-Mahler-conjecture-and-its-equality-cases-September-22-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/087.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "087:The-Mahler-Conjecture-for-General-Convex-Bodies-September-22-2026",
      "family_id": "087",
      "discipline": "Convex and metric geometry",
      "title": "The Mahler Conjecture for General Convex Bodies",
      "pdf_path": "preprints/The-Mahler-Conjecture-for-General-Convex-Bodies-September-22-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Mahler-Conjecture-for-General-Convex-Bodies-September-22-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/087.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "087:Symplectic-Balls-in-Symmetric-Polar-Products-September-22-2026",
      "family_id": "087",
      "discipline": "Convex and metric geometry",
      "title": "Symplectic Balls in Symmetric Polar Products",
      "pdf_path": "preprints/Symplectic-Balls-in-Symmetric-Polar-Products-September-22-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Symplectic-Balls-in-Symmetric-Polar-Products-September-22-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/087.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "088:Pettys-projection-volume-conjecture-in-dimensions-at-least-four-September-24-2026",
      "family_id": "088",
      "discipline": "Convex and metric geometry",
      "title": "Petty\u2019s projection-volume conjecture in dimensions at least four",
      "pdf_path": "preprints/Pettys-projection-volume-conjecture-in-dimensions-at-least-four-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Pettys-projection-volume-conjecture-in-dimensions-at-least-four-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/088.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "088:A-product-counterexample-to-the-simplex-maximum-for-projection-body-volume-September-24-2026",
      "family_id": "088",
      "discipline": "Convex and metric geometry",
      "title": "A product counterexample to the simplex maximum for projection-body volume",
      "pdf_path": "preprints/A-product-counterexample-to-the-simplex-maximum-for-projection-body-volume-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-product-counterexample-to-the-simplex-maximum-for-projection-body-volume-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/088.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "089:Planar-Graph-Metrics-Embed-into-L1-with-Constant-Distortion-September-23-2026",
      "family_id": "089",
      "discipline": "Convex and metric geometry",
      "title": "Planar Graph Metrics Embed into L1 with Constant Distortion",
      "pdf_path": "preprints/Planar-Graph-Metrics-Embed-into-L1-with-Constant-Distortion-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Planar-Graph-Metrics-Embed-into-L1-with-Constant-Distortion-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/089.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "089:L1-Embeddings-of-Graphs-of-Bounded-Treewidth-September-23-2026",
      "family_id": "089",
      "discipline": "Convex and metric geometry",
      "title": "L1 Embeddings of Graphs of Bounded Treewidth",
      "pdf_path": "preprints/L1-Embeddings-of-Graphs-of-Bounded-Treewidth-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/L1-Embeddings-of-Graphs-of-Bounded-Treewidth-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/089.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "090:An-atomic-certificate-for-triangular-lattice-universal-optimality-September-26-2026",
      "family_id": "090",
      "discipline": "Convex and metric geometry",
      "title": "An atomic certificate for triangular-lattice universal optimality",
      "pdf_path": "preprints/An-atomic-certificate-for-triangular-lattice-universal-optimality-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-atomic-certificate-for-triangular-lattice-universal-optimality-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/090.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "090:Universal-optimality-of-the-triangular-lattice-September-23-2026",
      "family_id": "090",
      "discipline": "Convex and metric geometry",
      "title": "Universal optimality of the triangular lattice",
      "pdf_path": "preprints/Universal-optimality-of-the-triangular-lattice-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Universal-optimality-of-the-triangular-lattice-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/090.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "090:A-sharp-Fourier-certificate-for-planar-circle-packing-September-23-2026",
      "family_id": "090",
      "discipline": "Convex and metric geometry",
      "title": "A sharp Fourier certificate for planar circle packing",
      "pdf_path": "preprints/A-sharp-Fourier-certificate-for-planar-circle-packing-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-sharp-Fourier-certificate-for-planar-circle-packing-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/090.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "090:Triangular-minimality-for-planar-Coulomb-renormalized-energy-September-23-2026",
      "family_id": "090",
      "discipline": "Convex and metric geometry",
      "title": "Triangular minimality for planar Coulomb renormalized energy",
      "pdf_path": "preprints/Triangular-minimality-for-planar-Coulomb-renormalized-energy-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Triangular-minimality-for-planar-Coulomb-renormalized-energy-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/090.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "091:The-logarithmic-Brunn-Minkowski-conjecture-September-23-2026",
      "family_id": "091",
      "discipline": "Convex and metric geometry",
      "title": "The logarithmic Brunn\u2013Minkowski conjecture",
      "pdf_path": "preprints/The-logarithmic-Brunn-Minkowski-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-logarithmic-Brunn-Minkowski-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/091.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "092:A-single-lattice-covering-bound-of-order-n-log-n-September-23-2026",
      "family_id": "092",
      "discipline": "Convex and metric geometry",
      "title": "A single-lattice covering bound of order n log n",
      "pdf_path": "preprints/A-single-lattice-covering-bound-of-order-n-log-n-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-single-lattice-covering-bound-of-order-n-log-n-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/092.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "092:Translative-covering-densities-of-order-n-log-n-September-23-2026",
      "family_id": "092",
      "discipline": "Convex and metric geometry",
      "title": "Translative covering densities of order n log n",
      "pdf_path": "preprints/Translative-covering-densities-of-order-n-log-n-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Translative-covering-densities-of-order-n-log-n-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/092.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "093:A-dimension-free-logarithmic-Sobolev-inequality-for-subgaussian-log-concave-measures-September-23-2026",
      "family_id": "093",
      "discipline": "Convex and metric geometry",
      "title": "A dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures",
      "pdf_path": "preprints/A-dimension-free-logarithmic-Sobolev-inequality-for-subgaussian-log-concave-measures-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-dimension-free-logarithmic-Sobolev-inequality-for-subgaussian-log-concave-measures-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "094:Subpolynomial-dimension-reduction-in-Lp-September-23-2026",
      "family_id": "094",
      "discipline": "Convex and metric geometry",
      "title": "Subpolynomial dimension reduction in Lp",
      "pdf_path": "preprints/Subpolynomial-dimension-reduction-in-Lp-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Subpolynomial-dimension-reduction-in-Lp-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/094.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "095:Hyperbolicity-Cones-Without-Semidefinite-Lifts-October-5-2026",
      "family_id": "095",
      "discipline": "Convex and metric geometry",
      "title": "Hyperbolicity Cones Without Semidefinite Lifts",
      "pdf_path": "preprints/Hyperbolicity-Cones-Without-Semidefinite-Lifts-October-5-2026/nonliftable-hyperbolicity.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Hyperbolicity-Cones-Without-Semidefinite-Lifts-October-5-2026/nonliftable-hyperbolicity.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/095.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "095:A-Nonspectrahedral-Hyperbolicity-Cone-September-24-2026",
      "family_id": "095",
      "discipline": "Convex and metric geometry",
      "title": "A nonspectrahedral hyperbolicity cone",
      "pdf_path": "preprints/A-Nonspectrahedral-Hyperbolicity-Cone-September-24-2026/nonspectrahedral-hyperbolicity-cone.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Nonspectrahedral-Hyperbolicity-Cone-September-24-2026/nonspectrahedral-hyperbolicity-cone.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/095.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "095:An-Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone-October-5-2026",
      "family_id": "095",
      "discipline": "Convex and metric geometry",
      "title": "An Exact Semidefinite Lift of a Nonspectrahedral Hyperbolicity Cone",
      "pdf_path": "preprints/An-Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone-October-5-2026/Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone-October-5-2026/Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/095.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "096:The-Gaussian-Propeller-Bound-in-Every-Dimension-September-24-2026",
      "family_id": "096",
      "discipline": "Convex and metric geometry",
      "title": "The Gaussian propeller bound in every dimension",
      "pdf_path": "preprints/The-Gaussian-Propeller-Bound-in-Every-Dimension-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Gaussian-Propeller-Bound-in-Every-Dimension-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/096.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "097:The-Euclidean-Steinitz-Bergstrom-theorem-September-24-2026",
      "family_id": "097",
      "discipline": "Convex and metric geometry",
      "title": "The Euclidean Steinitz\u2013Bergstr\u00f6m theorem",
      "pdf_path": "preprints/The-Euclidean-Steinitz-Bergstrom-theorem-September-24-2026/The-Euclidean-Steinitz-Bergstrom-theorem-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Euclidean-Steinitz-Bergstrom-theorem-September-24-2026/The-Euclidean-Steinitz-Bergstrom-theorem-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/097.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "098:A-doubling-Hilbert-subset-with-no-finite-dimensional-bi-Lipschitz-embedding-September-25-2026",
      "family_id": "098",
      "discipline": "Convex and metric geometry",
      "title": "A doubling Hilbert subset with no finite-dimensional bi-Lipschitz embedding",
      "pdf_path": "preprints/A-doubling-Hilbert-subset-with-no-finite-dimensional-bi-Lipschitz-embedding-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-doubling-Hilbert-subset-with-no-finite-dimensional-bi-Lipschitz-embedding-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/098.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "099:Edit-Distance-in-l1-Matching-Bounds-up-to-Constants-in-the-Exponent-September-27-2026",
      "family_id": "099",
      "discipline": "Convex and metric geometry",
      "title": "Edit Distance in l1: Matching Bounds up to Constants in the Exponent",
      "pdf_path": "preprints/Edit-Distance-in-l1-Matching-Bounds-up-to-Constants-in-the-Exponent-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Edit-Distance-in-l1-Matching-Bounds-up-to-Constants-in-the-Exponent-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/099.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "099:Finite-Circle-Obstructions-Binary-Codes-and-Histogram-Embeddings-for-Edit-Distance-September-27-2026",
      "family_id": "099",
      "discipline": "Convex and metric geometry",
      "title": "Finite-Circle Obstructions, Binary Codes, and Histogram Embeddings for Edit Distance",
      "pdf_path": "preprints/Finite-Circle-Obstructions-Binary-Codes-and-Histogram-Embeddings-for-Edit-Distance-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-Circle-Obstructions-Binary-Codes-and-Histogram-Embeddings-for-Edit-Distance-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/099.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "099:Tree-Constructions-for-the-l1-Distortion-of-Binary-Edit-Distance-September-27-2026",
      "family_id": "099",
      "discipline": "Convex and metric geometry",
      "title": "Tree Constructions for the l1 Distortion of Binary Edit Distance",
      "pdf_path": "preprints/Tree-Constructions-for-the-l1-Distortion-of-Binary-Edit-Distance-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Tree-Constructions-for-the-l1-Distortion-of-Binary-Edit-Distance-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/099.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "100:Finite-angular-cylinder-covers-below-the-half-area-bound-September-27-2026",
      "family_id": "100",
      "discipline": "Convex and metric geometry",
      "title": "Finite angular cylinder covers below the half-area bound",
      "pdf_path": "preprints/Finite-angular-cylinder-covers-below-the-half-area-bound-September-27-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-angular-cylinder-covers-below-the-half-area-bound-September-27-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/100.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "100:Finite-cylinder-approximation-of-ruled-sets-September-27-2026",
      "family_id": "100",
      "discipline": "Convex and metric geometry",
      "title": "Finite cylinder approximation of ruled sets",
      "pdf_path": "preprints/Finite-cylinder-approximation-of-ruled-sets-September-27-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-cylinder-approximation-of-ruled-sets-September-27-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/100.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "100:Slope-field-perturbations-of-the-two-cylinder-covering-September-27-2026",
      "family_id": "100",
      "discipline": "Convex and metric geometry",
      "title": "Slope-field perturbations of the two-cylinder covering",
      "pdf_path": "preprints/Slope-field-perturbations-of-the-two-cylinder-covering-September-27-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Slope-field-perturbations-of-the-two-cylinder-covering-September-27-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/100.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "100:Finite-triangular-approximation-of-radial-sweeps-September-27-2026",
      "family_id": "100",
      "discipline": "Convex and metric geometry",
      "title": "Finite triangular approximation of radial sweeps",
      "pdf_path": "preprints/Finite-triangular-approximation-of-radial-sweeps-September-27-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-triangular-approximation-of-radial-sweeps-September-27-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/100.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "101:A-sharp-entropy-bound-and-the-simplex-inequality-for-isotropic-constants-October-5-2026",
      "family_id": "101",
      "discipline": "Convex and metric geometry",
      "title": "A sharp entropy bound and the simplex inequality for isotropic constants",
      "pdf_path": "preprints/A-sharp-entropy-bound-and-the-simplex-inequality-for-isotropic-constants-October-5-2026/isotropic-simplex.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-sharp-entropy-bound-and-the-simplex-inequality-for-isotropic-constants-October-5-2026/isotropic-simplex.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "102:The-Unique-Games-Theorem-September-23-2026",
      "family_id": "102",
      "discipline": "Theoretical computer science",
      "title": "The Unique Games Theorem",
      "pdf_path": "preprints/The-Unique-Games-Theorem-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Unique-Games-Theorem-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/102.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "102:A-Direct-Proof-of-Optimal-Max-Cut-Hardness-September-23-2026",
      "family_id": "102",
      "discipline": "Theoretical computer science",
      "title": "A Direct Proof of Optimal Max-Cut Hardness",
      "pdf_path": "preprints/A-Direct-Proof-of-Optimal-Max-Cut-Hardness-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Direct-Proof-of-Optimal-Max-Cut-Hardness-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/102.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "102:The-Factor-Two-Hardness-Threshold-for-Vertex-Cover-September-23-2026",
      "family_id": "102",
      "discipline": "Theoretical computer science",
      "title": "The Factor-Two Hardness Threshold for Vertex Cover",
      "pdf_path": "preprints/The-Factor-Two-Hardness-Threshold-for-Vertex-Cover-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Factor-Two-Hardness-Threshold-for-Vertex-Cover-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/102.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "102:Constant-factor-hardness-of-Min-UnCut-September-23-2026",
      "family_id": "102",
      "discipline": "Theoretical computer science",
      "title": "Constant-factor hardness of Min-UnCut",
      "pdf_path": "preprints/Constant-factor-hardness-of-Min-UnCut-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Constant-factor-hardness-of-Min-UnCut-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/102.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "102:Constant-factor-hardness-of-directed-feedback-vertex-set-September-23-2026",
      "family_id": "102",
      "discipline": "Theoretical computer science",
      "title": "Constant-factor hardness of directed feedback vertex set",
      "pdf_path": "preprints/Constant-factor-hardness-of-directed-feedback-vertex-set-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Constant-factor-hardness-of-directed-feedback-vertex-set-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/102.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "103:Exact-Derandomization-of-Logarithmic-Space-L-equals-RL-equals-BPL-September-23-2026",
      "family_id": "103",
      "discipline": "Theoretical computer science",
      "title": "Exact derandomization of logarithmic space: L = RL = BPL",
      "pdf_path": "preprints/Exact-Derandomization-of-Logarithmic-Space-L-equals-RL-equals-BPL-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-Derandomization-of-Logarithmic-Space-L-equals-RL-equals-BPL-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Exact-Derandomization-of-Logarithmic-Space-L-equals-RL-equals-BPL-September-23-2026/build/sections/introduction.tex",
          "extent": "full introduction",
          "note": "Decision/model scope and probability approximation; general precision costs exponential in unary accuracy.",
          "sha256": "21e5c9742800d38df65575b5577627046dd59d2f220e8987b7fca1d2cfb7a6bc"
        },
        {
          "path": "preprints/Exact-Derandomization-of-Logarithmic-Space-L-equals-RL-equals-BPL-September-23-2026/build/sections/model.tex",
          "extent": "full transition model/resource section",
          "note": "Time-layered substochastic configuration graph, exact accepting-coordinate interpretation and machine-dependent constants.",
          "sha256": "dff70ae5f6922daf34dbb1f11ba57a11c0d6a18e7281c8288a154b429855e9d9"
        },
        {
          "path": "preprints/Exact-Derandomization-of-Logarithmic-Space-L-equals-RL-equals-BPL-September-23-2026/build/sections/compiler.tex",
          "extent": "full effective compiler section",
          "note": "Supplied resource promises, fixed library, virtual padding and explicit simultaneous numerical bounds; no execution.",
          "sha256": "c9edf110e23b522052f88b76e0f4dd586a153f566d32f0d4d2b704ab74537d95"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/103.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "104:Turn-Based-Stochastic-Mean-Payoff-Games-in-Deterministic-Quasipolynomial-Time-October-5-2026",
      "family_id": "104",
      "discipline": "Theoretical computer science",
      "title": "Turn-Based Stochastic Mean-Payoff Games in Deterministic Quasipolynomial Time",
      "pdf_path": "preprints/Turn-Based-Stochastic-Mean-Payoff-Games-in-Deterministic-Quasipolynomial-Time-October-5-2026/stochastic-mean-payoff-games.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Turn-Based-Stochastic-Mean-Payoff-Games-in-Deterministic-Quasipolynomial-Time-October-5-2026/stochastic-mean-payoff-games.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/104.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "104:Mean-payoff-parity-games-in-quasipolynomial-time-October-5-2026",
      "family_id": "104",
      "discipline": "Theoretical computer science",
      "title": "Mean-payoff parity games in quasipolynomial time",
      "pdf_path": "preprints/Mean-payoff-parity-games-in-quasipolynomial-time-October-5-2026/mean-payoff-parity.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Mean-payoff-parity-games-in-quasipolynomial-time-October-5-2026/mean-payoff-parity.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/104.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "104:Deterministic-quasipolynomial-time-mean-payoff-games-September-25-2026",
      "family_id": "104",
      "discipline": "Theoretical computer science",
      "title": "Deterministic quasipolynomial-time mean-payoff games",
      "pdf_path": "preprints/Deterministic-quasipolynomial-time-mean-payoff-games-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Deterministic-quasipolynomial-time-mean-payoff-games-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/104.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "104:Randomized-quasipolynomial-time-mean-payoff-games-September-25-2026",
      "family_id": "104",
      "discipline": "Theoretical computer science",
      "title": "Randomized quasipolynomial-time mean-payoff games",
      "pdf_path": "preprints/Randomized-quasipolynomial-time-mean-payoff-games-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Randomized-quasipolynomial-time-mean-payoff-games-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/104.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "105:Perfect-completeness-for-2-to-1-games-September-23-2026",
      "family_id": "105",
      "discipline": "Theoretical computer science",
      "title": "Perfect completeness for 2-to-1 games",
      "pdf_path": "preprints/Perfect-completeness-for-2-to-1-games-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Perfect-completeness-for-2-to-1-games-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/105.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "106:Hardness-of-finding-large-independent-sets-in-three-colorable-graphs-September-24-2026",
      "family_id": "106",
      "discipline": "Theoretical computer science",
      "title": "Hardness of finding large independent sets in three-colorable graphs",
      "pdf_path": "preprints/Hardness-of-finding-large-independent-sets-in-three-colorable-graphs-September-24-2026/Hardness-of-finding-large-independent-sets-in-three-colorable-graphs-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Hardness-of-finding-large-independent-sets-in-three-colorable-graphs-September-24-2026/Hardness-of-finding-large-independent-sets-in-three-colorable-graphs-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/106.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "107:Matrix-Multiplication-Nine-Fourths-October-2-2026",
      "family_id": "107",
      "discipline": "Theoretical computer science",
      "title": "An Upper Bound of 9/4 for the Matrix Multiplication Exponent",
      "pdf_path": "preprints/Matrix-Multiplication-Nine-Fourths-October-2-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Matrix-Multiplication-Nine-Fourths-October-2-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/107.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "107:Complex-Matrix-Multiplication-Below-2.258-and-Rectangular-Bounds-September-24-2026",
      "family_id": "107",
      "discipline": "Theoretical computer science",
      "title": "Complex Matrix Multiplication Below 2.258 and Rectangular Bounds",
      "pdf_path": "preprints/Complex-Matrix-Multiplication-Below-2.258-and-Rectangular-Bounds-September-24-2026/Complex-Matrix-Multiplication-Below-2.258-and-Rectangular-Bounds-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Complex-Matrix-Multiplication-Below-2.258-and-Rectangular-Bounds-September-24-2026/Complex-Matrix-Multiplication-Below-2.258-and-Rectangular-Bounds-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/107.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "107:Staggered-extraction-for-exact-matrix-multiplication-over-every-field-September-24-2026",
      "family_id": "107",
      "discipline": "Theoretical computer science",
      "title": "Staggered extraction for exact matrix multiplication over every field",
      "pdf_path": "preprints/Staggered-extraction-for-exact-matrix-multiplication-over-every-field-September-24-2026/Staggered-extraction-for-exact-matrix-multiplication-over-every-field-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Staggered-extraction-for-exact-matrix-multiplication-over-every-field-September-24-2026/Staggered-extraction-for-exact-matrix-multiplication-over-every-field-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/107.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "108:A-cubic-lower-bound-for-border-determinantal-complexity-of-the-permanent-September-24-2026",
      "family_id": "108",
      "discipline": "Theoretical computer science",
      "title": "A cubic lower bound for border determinantal complexity of the permanent",
      "pdf_path": "preprints/A-cubic-lower-bound-for-border-determinantal-complexity-of-the-permanent-September-24-2026/A-cubic-lower-bound-for-border-determinantal-complexity-of-the-permanent-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-cubic-lower-bound-for-border-determinantal-complexity-of-the-permanent-September-24-2026/A-cubic-lower-bound-for-border-determinantal-complexity-of-the-permanent-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/108.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "109:Integer-multiplication-below-n-log-n-September-23-2026",
      "family_id": "109",
      "discipline": "Theoretical computer science",
      "title": "Integer multiplication below n log n",
      "pdf_path": "preprints/Integer-multiplication-below-n-log-n-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Integer-multiplication-below-n-log-n-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "110:Squared-logarithmic-randomized-k-server-on-arbitrary-metrics-September-24-2026",
      "family_id": "110",
      "discipline": "Theoretical computer science",
      "title": "Squared-logarithmic randomized k-server on arbitrary metrics",
      "pdf_path": "preprints/Squared-logarithmic-randomized-k-server-on-arbitrary-metrics-September-24-2026/Squared-logarithmic-randomized-k-server-on-arbitrary-metrics-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Squared-logarithmic-randomized-k-server-on-arbitrary-metrics-September-24-2026/Squared-logarithmic-randomized-k-server-on-arbitrary-metrics-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/110.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "110:Uniform-computation-of-the-squared-logarithmic-k-server-bound-September-24-2026",
      "family_id": "110",
      "discipline": "Theoretical computer science",
      "title": "Uniform computation of the squared-logarithmic k-server bound",
      "pdf_path": "preprints/Uniform-computation-of-the-squared-logarithmic-k-server-bound-September-24-2026/Uniform-computation-of-the-squared-logarithmic-k-server-bound-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-computation-of-the-squared-logarithmic-k-server-bound-September-24-2026/Uniform-computation-of-the-squared-logarithmic-k-server-bound-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Uniform-computation-of-the-squared-logarithmic-k-server-bound-September-24-2026/build/source/sections/01-introduction.tex",
          "extent": "full introduction",
          "note": "Uniform finite-rational-metric theorem with unrestricted additive loss and request-counter time dependence.",
          "sha256": "40fcd20a5d130ad572090dffffd054923fe4809a07a3d3282a5b4c8fe281f619"
        },
        {
          "path": "preprints/Uniform-computation-of-the-squared-logarithmic-k-server-bound-September-24-2026/build/source/sections/04-uniform-computation.tex",
          "extent": "full uniform scheduling section",
          "note": "Exact activation 2^T_P-1, constructor/output schedule and displayed additive constant.",
          "sha256": "1910910ef41491c73d562e368976ca3e44ef6c21b8b6746b6f55f19f292b69b3"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/110.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "111:One-Sample-Suffices-for-Matroid-Prophet-Inequalities-against-an-Almighty-Adversary-September-23-2026",
      "family_id": "111",
      "discipline": "Theoretical computer science",
      "title": "One Sample Suffices for Matroid Prophet Inequalities against an Almighty Adversary",
      "pdf_path": "preprints/One-Sample-Suffices-for-Matroid-Prophet-Inequalities-against-an-Almighty-Adversary-September-23-2026/final.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/One-Sample-Suffices-for-Matroid-Prophet-Inequalities-against-an-Almighty-Adversary-September-23-2026/final.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/111.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "112:Beyond-the-Square-Root-Exponent-for-Depth-Three-Boolean-Circuits-September-23-2026",
      "family_id": "112",
      "discipline": "Theoretical computer science",
      "title": "Beyond the Square-Root Exponent for Depth-Three Boolean Circuits",
      "pdf_path": "preprints/Beyond-the-Square-Root-Exponent-for-Depth-Three-Boolean-Circuits-September-23-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Beyond-the-Square-Root-Exponent-for-Depth-Three-Boolean-Circuits-September-23-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/112.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "113:A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026",
      "family_id": "113",
      "discipline": "Theoretical computer science",
      "title": "A Fully Polynomial Randomized Approximation Scheme for Perfect Matchings in General Graphs",
      "pdf_path": "preprints/A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026/build/main.tex",
          "extent": "lines 1\u2013250; 2350\u20132725; 2820\u20132845; 3080\u20133140",
          "note": "Abstract/main statement, part of introduction, sampler guarantee and counting schedules, amplification and prescribed-degree corollary. Full proof/bit implementation and deletion sampler not independently checked.",
          "sha256": "dcf28553d442dfc53a9f90f7c52bd48c9e2e7e5e27b197aa7ca4be1c8daed703"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/113.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "113:Entropy-and-Face-Dimension-of-the-Perfect-Matching-Polytope-September-23-2026",
      "family_id": "113",
      "discipline": "Theoretical computer science",
      "title": "Entropy and Face Dimension of the Perfect-Matching Polytope",
      "pdf_path": "preprints/Entropy-and-Face-Dimension-of-the-Perfect-Matching-Polytope-September-23-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Entropy-and-Face-Dimension-of-the-Perfect-Matching-Polytope-September-23-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Entropy-and-Face-Dimension-of-the-Perfect-Matching-Polytope-September-23-2026/build/sections/01-introduction.tex",
          "extent": "lines 1\u2013240",
          "note": "Pointwise entropy, face-dimension and deterministic counting statements; large-degree polynomial and 512^n approximation limits.",
          "sha256": "b5dac47840e40de4d2b31a3cbe326544fcb0612d33625676b5c632837ec435ce"
        },
        {
          "path": "preprints/Entropy-and-Face-Dimension-of-the-Perfect-Matching-Polytope-September-23-2026/build/sections/09-algorithm.tex",
          "extent": "lines 1\u2013155",
          "note": "Selected exact algorithm schedule and guarantee; no full implementation or proof check.",
          "sha256": "b328441fc52680cff5438841bd394a0ad2a614e0dca13ed57b9f321bdb71f824"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/113.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "114:An-FPRAS-for-Common-Integer-Polymatroid-Bases-with-Binary-Capacities-October-5-2026",
      "family_id": "114",
      "discipline": "Theoretical computer science",
      "title": "An FPRAS for Common Integer Polymatroid Bases with Binary Capacities",
      "pdf_path": "preprints/An-FPRAS-for-Common-Integer-Polymatroid-Bases-with-Binary-Capacities-October-5-2026/polymatroid-fpras.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-FPRAS-for-Common-Integer-Polymatroid-Bases-with-Binary-Capacities-October-5-2026/polymatroid-fpras.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/114.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "114:Approximate-counting-of-common-bases-of-two-matroids-September-23-2026",
      "family_id": "114",
      "discipline": "Theoretical computer science",
      "title": "Approximate counting of common bases of two matroids",
      "pdf_path": "preprints/Approximate-counting-of-common-bases-of-two-matroids-September-23-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Approximate-counting-of-common-bases-of-two-matroids-September-23-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/114.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "115:Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026",
      "family_id": "115",
      "discipline": "Theoretical computer science",
      "title": "Exact Uniform Sampling of Contingency Tables with Arbitrary Margins",
      "pdf_path": "preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026/build/sections/introduction.tex",
          "extent": "introduction",
          "note": "Literal schedules and sampling model reviewed; full proof not independently checked.",
          "sha256": "173a0eaf3df62e2e7833be0b13abbaa4db0650f082c77a3d1faddda9ed65f242"
        },
        {
          "path": "preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026/build/sections/model-and-graph.tex",
          "extent": "parameter block",
          "note": "Literal schedules and sampling model reviewed; full proof not independently checked.",
          "sha256": "417050fcb6ad3f4830ae339fbc7c0078d87f960fa438d0c8ce1dfd03d45afc4b"
        },
        {
          "path": "preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026/build/sections/algorithms.tex",
          "extent": "outer schedule, exact law tabulation and rare correction",
          "note": "Literal schedules and sampling model reviewed; full proof not independently checked.",
          "sha256": "ed5a846b4d6de2ff2ea2bed21aaa441107115e0a2745328cd3413e5a963c8a46"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/115.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "115:An-FPRAS-for-Cell-Bounded-Contingency-Tables-September-24-2026",
      "family_id": "115",
      "discipline": "Theoretical computer science",
      "title": "An FPRAS for Cell-Bounded Contingency Tables",
      "pdf_path": "preprints/An-FPRAS-for-Cell-Bounded-Contingency-Tables-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-FPRAS-for-Cell-Bounded-Contingency-Tables-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/An-FPRAS-for-Cell-Bounded-Contingency-Tables-September-24-2026/build/sections/introduction.tex",
          "extent": "introduction",
          "note": "Each bounded table counted once; structural zeros; complexity rather than practical runtime.",
          "sha256": "dcbce0a815f690246a36b1f0d4268d6f4fbce105b0364267d067e642541bb730"
        },
        {
          "path": "preprints/An-FPRAS-for-Cell-Bounded-Contingency-Tables-September-24-2026/build/sections/scales.tex",
          "extent": "tightening and scale definitions",
          "note": "Each bounded table counted once; structural zeros; complexity rather than practical runtime.",
          "sha256": "062476901a2c6074f1258fcfffc9f29d245b937d940e1b0f52c26b9cde43a7f4"
        },
        {
          "path": "preprints/An-FPRAS-for-Cell-Bounded-Contingency-Tables-September-24-2026/build/sections/algorithm.tex",
          "extent": "selected phase schedule",
          "note": "Each bounded table counted once; structural zeros; complexity rather than practical runtime.",
          "sha256": "d72275b30bfe8eff994258929d797f3d3c5203b3bdc8d252b903032f48c744f8"
        },
        {
          "path": "preprints/An-FPRAS-for-Cell-Bounded-Contingency-Tables-September-24-2026/build/sections/flows.tex",
          "extent": "entire 209-line section",
          "note": "Full source flow-to-table bijection and approximate sampling self-reduction read. Paper-level text review, not independent proof acceptance.",
          "sha256": "07de54a84f723132480bbe349492638e273a80e2184674035c129ee8883c00a8"
        },
        {
          "path": "preprints/An-FPRAS-for-Cell-Bounded-Contingency-Tables-September-24-2026/build/sections/history.tex",
          "extent": "entire 92-line section",
          "note": "Prior regimes, graph-flow consequence and accuracy distinction read; cited antecedents not all independently rechecked.",
          "sha256": "55c3137f352a7da90b1a4a5742066c60f538cd8e1acd0b2040ef5b25b3b37566"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/115.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "116:Uniform-Matrix-Hitting-Points-in-Every-Positive-Characteristic-October-4-2026",
      "family_id": "116",
      "discipline": "Theoretical computer science",
      "title": "Uniform Matrix Hitting Points in Every Positive Characteristic",
      "pdf_path": "preprints/Uniform-Matrix-Hitting-Points-in-Every-Positive-Characteristic-October-4-2026/uniform-matrix-hitting-points-positive-characteristic.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-Matrix-Hitting-Points-in-Every-Positive-Characteristic-October-4-2026/uniform-matrix-hitting-points-positive-characteristic.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Uniform-Matrix-Hitting-Points-in-Every-Positive-Characteristic-October-4-2026/uniform-matrix-hitting-points-positive-characteristic.pdf",
          "extent": "PDF pages 1-4 and 10-13; visual page 12",
          "sha256": "06284554d3db1df4569dff00d12df083815bf1bafc401f9c97f4ba9cc09119fc",
          "note": "Reading scope only; source proof/Lean/program acceptance incomplete."
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/116.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "116:One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026",
      "family_id": "116",
      "discipline": "Theoretical computer science",
      "title": "One Rational Matrix Hitting Point for Noncommutative Formulas",
      "pdf_path": "preprints/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026.pdf",
          "extent": "PDF pages 1-12; visual pages 10,11; final reference page 13 not separately reviewed",
          "sha256": "984d0d4287bc29fc4772a2254aabafb9ee8886c56eeafeef0a746c7fc06869ed",
          "note": "Reading scope only; source proof/Lean/program acceptance incomplete."
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/116.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "116:Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026",
      "family_id": "116",
      "discipline": "Theoretical computer science",
      "title": "Polynomial Hitting Lists for Noncommutative Rational Formulas",
      "pdf_path": "preprints/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026.pdf",
          "extent": "PDF pages 1-4 and 16-21; visual pages 16,17",
          "sha256": "8f6fe5057bd59278bfb88ccf38342c09602e547f35a757b8eadc30ece76cec0e",
          "note": "Reading scope only; source proof/Lean/program acceptance incomplete."
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/116.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "117:Constant-factor-hardness-of-uniform-sparsest-cut-September-24-2026",
      "family_id": "117",
      "discipline": "Theoretical computer science",
      "title": "Constant-factor hardness of uniform sparsest cut",
      "pdf_path": "preprints/Constant-factor-hardness-of-uniform-sparsest-cut-September-24-2026/Constant-factor-hardness-of-uniform-sparsest-cut-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Constant-factor-hardness-of-uniform-sparsest-cut-September-24-2026/Constant-factor-hardness-of-uniform-sparsest-cut-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/117.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "117:Near-square-root-logarithmic-integrality-gaps-for-uniform-sparsest-cut-September-24-2026",
      "family_id": "117",
      "discipline": "Theoretical computer science",
      "title": "Near-square-root logarithmic integrality gaps for uniform sparsest cut",
      "pdf_path": "preprints/Near-square-root-logarithmic-integrality-gaps-for-uniform-sparsest-cut-September-24-2026/Near-square-root-logarithmic-integrality-gaps-for-uniform-sparsest-cut-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Near-square-root-logarithmic-integrality-gaps-for-uniform-sparsest-cut-September-24-2026/Near-square-root-logarithmic-integrality-gaps-for-uniform-sparsest-cut-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/117.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "118:Additive-hardness-and-unbounded-configuration-gaps-in-bin-packing-September-24-2026",
      "family_id": "118",
      "discipline": "Theoretical computer science",
      "title": "Additive hardness and unbounded configuration gaps in bin packing",
      "pdf_path": "preprints/Additive-hardness-and-unbounded-configuration-gaps-in-bin-packing-September-24-2026/Additive-hardness-and-unbounded-configuration-gaps-in-bin-packing-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Additive-hardness-and-unbounded-configuration-gaps-in-bin-packing-September-24-2026/Additive-hardness-and-unbounded-configuration-gaps-in-bin-packing-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/118.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "119:Sharp-binary-information-contraction-on-the-discrete-cube-September-24-2026",
      "family_id": "119",
      "discipline": "Theoretical computer science",
      "title": "Sharp binary-information contraction on the discrete cube",
      "pdf_path": "preprints/Sharp-binary-information-contraction-on-the-discrete-cube-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Sharp-binary-information-contraction-on-the-discrete-cube-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/119.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "119:Hellinger-contraction-with-arbitrary-Boolean-output-bias-September-24-2026",
      "family_id": "119",
      "discipline": "Theoretical computer science",
      "title": "Hellinger contraction with arbitrary Boolean output bias",
      "pdf_path": "preprints/Hellinger-contraction-with-arbitrary-Boolean-output-bias-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Hellinger-contraction-with-arbitrary-Boolean-output-bias-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/119.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "120:Almost-Linear-Time-Maximum-Cardinality-Matching-in-Sparse-General-Graphs-September-24-2026",
      "family_id": "120",
      "discipline": "Theoretical computer science",
      "title": "Almost-Linear-Time Maximum-Cardinality Matching in General Graphs",
      "pdf_path": "preprints/Almost-Linear-Time-Maximum-Cardinality-Matching-in-Sparse-General-Graphs-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Almost-Linear-Time-Maximum-Cardinality-Matching-in-Sparse-General-Graphs-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Almost-Linear-Time-Maximum-Cardinality-Matching-in-Sparse-General-Graphs-September-24-2026/build/sections/01-introduction.tex",
          "extent": "introduction",
          "note": "Necessary literal-backend size bound derived; early structural cases/fallback remain separate.",
          "sha256": "26eceebaac6b2ad869c9aa7451c9d57c98e835703130edbefc45a1a637503c22"
        },
        {
          "path": "preprints/Almost-Linear-Time-Maximum-Cardinality-Matching-in-Sparse-General-Graphs-September-24-2026/build/sections/05-engine.tex",
          "extent": "selected master-size block",
          "note": "Necessary literal-backend size bound derived; early structural cases/fallback remain separate.",
          "sha256": "939f221a14b39eee8ab0aca6417de5502983842c4f2d23579e00b4ea5f0885d3"
        },
        {
          "path": "preprints/Almost-Linear-Time-Maximum-Cardinality-Matching-in-Sparse-General-Graphs-September-24-2026/build/sections/07-backend-quality.tex",
          "extent": "backend parameters and guard block",
          "note": "Necessary literal-backend size bound derived; early structural cases/fallback remain separate.",
          "sha256": "01699a433457bc787331cc2e76f8e99aa7697206be49ab7a639d43653d379401"
        },
        {
          "path": "preprints/Almost-Linear-Time-Maximum-Cardinality-Matching-in-Sparse-General-Graphs-September-24-2026/build/sections/09-uniformization.tex",
          "extent": "uniform program",
          "note": "Necessary literal-backend size bound derived; early structural cases/fallback remain separate.",
          "sha256": "7c4f2d2ec41daf7f7d2113370d8f06c8f23de9ac87aa809135f357999342eed0"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "121:An-Almost-Linear-Approximation-Scheme-for-Edit-Distance-September-24-2026",
      "family_id": "121",
      "discipline": "Theoretical computer science",
      "title": "An Almost-Linear Approximation Scheme for Edit Distance",
      "pdf_path": "preprints/An-Almost-Linear-Approximation-Scheme-for-Edit-Distance-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-Almost-Linear-Approximation-Scheme-for-Edit-Distance-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/An-Almost-Linear-Approximation-Scheme-for-Edit-Distance-September-24-2026/paper.pdf",
          "sha256": "7ecda63faaa7d6a3ff36852775a6a015a8d832ace341a534af86a375d1d89807",
          "extent": "PDF pages 1-8, 34, 43 and concluding paragraph on 44; visual pages 7,8,34",
          "note": "Full 46-page extraction does not establish full reading; full proof/program acceptance incomplete."
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/121.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "122:Uniform-quasipolynomial-time-trace-reconstruction-October-5-2026",
      "family_id": "122",
      "discipline": "Theoretical computer science",
      "title": "Uniform quasipolynomial-time trace reconstruction",
      "pdf_path": "preprints/Uniform-quasipolynomial-time-trace-reconstruction-October-5-2026/uniform-trace-reconstruction.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-quasipolynomial-time-trace-reconstruction-October-5-2026/uniform-trace-reconstruction.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/122.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "122:A-latest-anchor-induction-with-spectrally-compact-masks-for-worst-case-trace-reconstruction-October-5-2026",
      "family_id": "122",
      "discipline": "Theoretical computer science",
      "title": "A latest-anchor induction with spectrally compact masks for worst-case trace reconstruction",
      "pdf_path": "preprints/A-latest-anchor-induction-with-spectrally-compact-masks-for-worst-case-trace-reconstruction-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-latest-anchor-induction-with-spectrally-compact-masks-for-worst-case-trace-reconstruction-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/122.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "122:quantitative-lower-bounds-for-trace-reconstruction-September-24-2026",
      "family_id": "122",
      "discipline": "Theoretical computer science",
      "title": "Quantitative lower bounds for trace reconstruction",
      "pdf_path": "preprints/quantitative-lower-bounds-for-trace-reconstruction-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/quantitative-lower-bounds-for-trace-reconstruction-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/122.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "124:A-polynomial-time-algorithm-for-three-machine-unit-job-scheduling-September-24-2026",
      "family_id": "124",
      "discipline": "Theoretical computer science",
      "title": "A Polynomial-Time Algorithm for Three-Machine Unit-Job Scheduling",
      "pdf_path": "preprints/A-polynomial-time-algorithm-for-three-machine-unit-job-scheduling-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-polynomial-time-algorithm-for-three-machine-unit-job-scheduling-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/A-polynomial-time-algorithm-for-three-machine-unit-job-scheduling-September-24-2026/build/paper.tex",
          "extent": "entire 541-line TeX source text file",
          "note": "Principal model/algorithm/invariant/complexity argument text read. Referenced figures, bibliography, source proof acceptance and formal imports remain uncompleted.",
          "sha256": "38f8318c45e578108367b3e35d87575ff0c1c56fb203d68a2d3b24b193eb6e2d"
        },
        {
          "path": "preprints/A-polynomial-time-algorithm-for-three-machine-unit-job-scheduling-September-24-2026/build/separators.tex",
          "extent": "entire 162-line TeX source text file",
          "note": "Principal model/algorithm/invariant/complexity argument text read. Referenced figures, bibliography, source proof acceptance and formal imports remain uncompleted.",
          "sha256": "9d97816e97a2df7708bcdf85a6422ec31db26ff76310358be2eaa759b70df23d"
        },
        {
          "path": "preprints/A-polynomial-time-algorithm-for-three-machine-unit-job-scheduling-September-24-2026/build/construction.tex",
          "extent": "entire 239-line TeX source text file",
          "note": "Principal model/algorithm/invariant/complexity argument text read. Referenced figures, bibliography, source proof acceptance and formal imports remain uncompleted.",
          "sha256": "06a715d2d1d7be615185488fad78760d15b1ab6883592dc68a6ecedac53195c9"
        },
        {
          "path": "preprints/A-polynomial-time-algorithm-for-three-machine-unit-job-scheduling-September-24-2026/build/lists.tex",
          "extent": "entire 372-line TeX source text file",
          "note": "Principal model/algorithm/invariant/complexity argument text read. Referenced figures, bibliography, source proof acceptance and formal imports remain uncompleted.",
          "sha256": "74338dbc16a0368ac60223797959713c55aa7f5a3aecc924a8cb9485a2f2bdf1"
        },
        {
          "path": "preprints/A-polynomial-time-algorithm-for-three-machine-unit-job-scheduling-September-24-2026/build/boundary.tex",
          "extent": "entire 168-line TeX source text file",
          "note": "Principal model/algorithm/invariant/complexity argument text read. Referenced figures, bibliography, source proof acceptance and formal imports remain uncompleted.",
          "sha256": "feccabc6bb4a6b3fcef859c607c4b2c93ff2621f06f98c87ab316751b79d6a03"
        },
        {
          "path": "preprints/A-polynomial-time-algorithm-for-three-machine-unit-job-scheduling-September-24-2026/build/descriptions.tex",
          "extent": "entire 203-line TeX source text file",
          "note": "Principal model/algorithm/invariant/complexity argument text read. Referenced figures, bibliography, source proof acceptance and formal imports remain uncompleted.",
          "sha256": "147e588e1b2f9e3eb89e688316a8394afafdd88fc14d50ee70a6e35262da629e"
        },
        {
          "path": "preprints/A-polynomial-time-algorithm-for-three-machine-unit-job-scheduling-September-24-2026/build/conclusion.tex",
          "extent": "entire 13-line TeX source text file",
          "note": "Principal model/algorithm/invariant/complexity argument text read. Referenced figures, bibliography, source proof acceptance and formal imports remain uncompleted.",
          "sha256": "917ac952a6a6eb47dbcae5b6ad00e1092f2962948feec46636cfbf1bf1d5e97c"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/124.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "125:Single-Exponential-Recovery-and-Bounded-Price-Strictness-for-Metric-k-Median-September-24-2026",
      "family_id": "125",
      "discipline": "Theoretical computer science",
      "title": "Single-exponential recovery and bounded-price strictness for metric k-median",
      "pdf_path": "preprints/Single-Exponential-Recovery-and-Bounded-Price-Strictness-for-Metric-k-Median-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Single-Exponential-Recovery-and-Bounded-Price-Strictness-for-Metric-k-Median-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Single-Exponential-Recovery-and-Bounded-Price-Strictness-for-Metric-k-Median-September-24-2026/paper.pdf",
          "extent": "PDF pages 1-6, abstract, introductory theorem promises, proof overview and normalization setup",
          "sha256": "823fdb284a7d3c0e3089869ba2da3d394db4f19b1c2ab56477ce6ae1b232614b",
          "note": "Selected pages only; extraction of other pages is not a reading record. Full proof and executable-source acceptance incomplete."
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/125.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "125:The-Approximation-Threshold-for-Metric-k-Median-September-24-2026",
      "family_id": "125",
      "discipline": "Theoretical computer science",
      "title": "The approximation threshold for metric k-median",
      "pdf_path": "preprints/The-Approximation-Threshold-for-Metric-k-Median-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Approximation-Threshold-for-Metric-k-Median-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/The-Approximation-Threshold-for-Metric-k-Median-September-24-2026/main.pdf",
          "extent": "PDF pages 1-5 and 27-35; pages 1,5,27,32,34 also visually inspected",
          "sha256": "c8176d1671beb83d3a459ff65e5c632d94364ec7e542930bf19fad0b75524d50",
          "note": "Selected pages only; extraction of other pages is not a reading record. Full proof and executable-source acceptance incomplete."
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/125.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "126:Exponential-PSD-rank-of-positively-shifted-matching-matrices-October-5-2026",
      "family_id": "126",
      "discipline": "Theoretical computer science",
      "title": "Exponential PSD rank of positively shifted matching matrices",
      "pdf_path": "preprints/Exponential-PSD-rank-of-positively-shifted-matching-matrices-October-5-2026/shifted-matching-psd.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exponential-PSD-rank-of-positively-shifted-matching-matrices-October-5-2026/shifted-matching-psd.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/126.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "127:Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026",
      "family_id": "127",
      "discipline": "Theoretical computer science",
      "title": "Average sensitivity of polynomial threshold functions",
      "pdf_path": "preprints/Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/127.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "128:A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026",
      "family_id": "128",
      "discipline": "Theoretical computer science",
      "title": "A Polynomial-Time 2-Approximation for Shortest Common Superstring",
      "pdf_path": "preprints/A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026/build/sections/01-introduction.tex",
          "extent": "entire 31-line TeX source file",
          "sha256": "bd57265f26ee2be8129f802fa07211d130e9ad85590fc62d27699fd065682803",
          "note": "Main model/count/layer/connection/group/cycle/complexity text read. Figures/bibliography/driver, imported proofs and independent acceptance remain uncompleted."
        },
        {
          "path": "preprints/A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026/build/sections/02-counts.tex",
          "extent": "entire 107-line TeX source file",
          "sha256": "9e4288a40029c9e20093c4af781f8b4848a8bd00d1326a5157b2dd340d7387e5",
          "note": "Main model/count/layer/connection/group/cycle/complexity text read. Figures/bibliography/driver, imported proofs and independent acceptance remain uncompleted."
        },
        {
          "path": "preprints/A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026/build/sections/03-layers.tex",
          "extent": "entire 117-line TeX source file",
          "sha256": "11709cc764d4583c4d539ac0fb341c7840f4520a0f53e1cddbb966b6846851de",
          "note": "Main model/count/layer/connection/group/cycle/complexity text read. Figures/bibliography/driver, imported proofs and independent acceptance remain uncompleted."
        },
        {
          "path": "preprints/A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026/build/sections/04-connections.tex",
          "extent": "entire 131-line TeX source file",
          "sha256": "4f1e01dea6ef53a6d9122670024b9ab551134ba76797dfb8d43a14fcbb90a1f1",
          "note": "Main model/count/layer/connection/group/cycle/complexity text read. Figures/bibliography/driver, imported proofs and independent acceptance remain uncompleted."
        },
        {
          "path": "preprints/A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026/build/sections/05-processing.tex",
          "extent": "entire 147-line TeX source file",
          "sha256": "412743cfff71f65b83f95bf49539a4241d4f9f9f922e1c77161884ed50d22802",
          "note": "Main model/count/layer/connection/group/cycle/complexity text read. Figures/bibliography/driver, imported proofs and independent acceptance remain uncompleted."
        },
        {
          "path": "preprints/A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026/build/sections/06-cycles.tex",
          "extent": "entire 68-line TeX source file",
          "sha256": "9c3712ce0863c387cc197f71c3454c9debe41fa9bdbc7339769216ad61e9dc83",
          "note": "Main model/count/layer/connection/group/cycle/complexity text read. Figures/bibliography/driver, imported proofs and independent acceptance remain uncompleted."
        },
        {
          "path": "preprints/A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026/build/sections/07-algorithm.tex",
          "extent": "entire 26-line TeX source file",
          "sha256": "e6b36f1f548f8b1db6694ce707d49b13b13f0f382a32e90af88bc8f91b0df4f9",
          "note": "Main model/count/layer/connection/group/cycle/complexity text read. Figures/bibliography/driver, imported proofs and independent acceptance remain uncompleted."
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/128.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "129:An-exponential-state-lower-bound-for-two-way-nondeterministic-complementation-September-25-2026",
      "family_id": "129",
      "discipline": "Theoretical computer science",
      "title": "An exponential state lower bound for two-way nondeterministic complementation",
      "pdf_path": "preprints/An-exponential-state-lower-bound-for-two-way-nondeterministic-complementation-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-exponential-state-lower-bound-for-two-way-nondeterministic-complementation-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/129.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "129:An-exponential-two-way-deterministic-state-lower-bound-for-one-way-liveness-September-25-2026",
      "family_id": "129",
      "discipline": "Theoretical computer science",
      "title": "An exponential two-way deterministic state lower bound for one-way liveness",
      "pdf_path": "preprints/An-exponential-two-way-deterministic-state-lower-bound-for-one-way-liveness-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-exponential-two-way-deterministic-state-lower-bound-for-one-way-liveness-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/129.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "130:An-explicit-power-saving-for-the-exact-discrete-Fourier-transform-September-25-2026",
      "family_id": "130",
      "discipline": "Theoretical computer science",
      "title": "An explicit power saving for the exact discrete Fourier transform",
      "pdf_path": "preprints/An-explicit-power-saving-for-the-exact-discrete-Fourier-transform-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-explicit-power-saving-for-the-exact-discrete-Fourier-transform-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/130.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "130:Finite-tensor-savings-and-exact-Fourier-circuits-September-25-2026",
      "family_id": "130",
      "discipline": "Theoretical computer science",
      "title": "Finite tensor savings and exact Fourier circuits",
      "pdf_path": "preprints/Finite-tensor-savings-and-exact-Fourier-circuits-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-tensor-savings-and-exact-Fourier-circuits-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/130.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "131:Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026",
      "family_id": "131",
      "discipline": "Theoretical computer science",
      "title": "Polynomial mixing of the switch chain for every graphical degree sequence",
      "pdf_path": "preprints/Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026/build/sections/introduction.tex",
          "extent": "full introduction/kernel",
          "note": "Read the complete introduction, pair-resampling setup, mixing derivation and exact sampling section, plus selected formal scope. The bound is for a precise half-hold/uniform-four-set/ordered-pair kernel on the complete host. All holding and rejected proposals count as steps. Host restrictions, directed/weighted or connected-only models need separate results. Exactness uses exponentially expensive rare residual tabulation in expectation and unbounded rejection draws; it is outside the selected formal chain estimates. The finite audit has a six-cycle-host disconnection example and an accepted-switch stationary-law example (triangle-event mass 1/5 versus uniform 1/7). These are small exact facts, not broad theorem verification. Dossier 005 is revised; literal cheap general certified sampling is deferred.",
          "sha256": "7c4684d2d3b698bf2be17088c17575e72a4588faf667bd71e2743430911a106f"
        },
        {
          "path": "preprints/Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026/build/sections/setup.tex",
          "extent": "full pair-resampling setup",
          "note": "Read the complete introduction, pair-resampling setup, mixing derivation and exact sampling section, plus selected formal scope. The bound is for a precise half-hold/uniform-four-set/ordered-pair kernel on the complete host. All holding and rejected proposals count as steps. Host restrictions, directed/weighted or connected-only models need separate results. Exactness uses exponentially expensive rare residual tabulation in expectation and unbounded rejection draws; it is outside the selected formal chain estimates. The finite audit has a six-cycle-host disconnection example and an accepted-switch stationary-law example (triangle-event mass 1/5 versus uniform 1/7). These are small exact facts, not broad theorem verification. Dossier 005 is revised; literal cheap general certified sampling is deferred.",
          "sha256": "0395b99be0ea02763e92785bff613c1cbf1b65a5e6adfcf295dbe3a07004f8da"
        },
        {
          "path": "preprints/Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026/build/sections/mixing.tex",
          "extent": "full mixing section",
          "note": "Read the complete introduction, pair-resampling setup, mixing derivation and exact sampling section, plus selected formal scope. The bound is for a precise half-hold/uniform-four-set/ordered-pair kernel on the complete host. All holding and rejected proposals count as steps. Host restrictions, directed/weighted or connected-only models need separate results. Exactness uses exponentially expensive rare residual tabulation in expectation and unbounded rejection draws; it is outside the selected formal chain estimates. The finite audit has a six-cycle-host disconnection example and an accepted-switch stationary-law example (triangle-event mass 1/5 versus uniform 1/7). These are small exact facts, not broad theorem verification. Dossier 005 is revised; literal cheap general certified sampling is deferred.",
          "sha256": "2b9d197997ca8126347c3ad93360243e55d6d0f761f1e02f8687023657b0fa55"
        },
        {
          "path": "preprints/Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026/build/sections/exact-sampling.tex",
          "extent": "full exact residual sampling section",
          "note": "Read the complete introduction, pair-resampling setup, mixing derivation and exact sampling section, plus selected formal scope. The bound is for a precise half-hold/uniform-four-set/ordered-pair kernel on the complete host. All holding and rejected proposals count as steps. Host restrictions, directed/weighted or connected-only models need separate results. Exactness uses exponentially expensive rare residual tabulation in expectation and unbounded rejection draws; it is outside the selected formal chain estimates. The finite audit has a six-cycle-host disconnection example and an accepted-switch stationary-law example (triangle-event mass 1/5 versus uniform 1/7). These are small exact facts, not broad theorem verification. Dossier 005 is revised; literal cheap general certified sampling is deferred.",
          "sha256": "369ea35e5d8b70815aa79710b08f972bc4d05a5590d20e8fa23fefb5c725c017"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/131.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "132:A-superquadratic-separation-between-sensitivity-and-block-sensitivity-September-25-2026",
      "family_id": "132",
      "discipline": "Theoretical computer science",
      "title": "A superquadratic separation between sensitivity and block sensitivity",
      "pdf_path": "preprints/A-superquadratic-separation-between-sensitivity-and-block-sensitivity-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-superquadratic-separation-between-sensitivity-and-block-sensitivity-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/132.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "133:Parity-lifts-and-bounded-treewidth-witnesses-for-Weisfeiler-Leman-equivalence-September-25-2026",
      "family_id": "133",
      "discipline": "Theoretical computer science",
      "title": "Parity lifts and bounded-treewidth witnesses for Weisfeiler\u2013Leman equivalence",
      "pdf_path": "preprints/Parity-lifts-and-bounded-treewidth-witnesses-for-Weisfeiler-Leman-equivalence-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Parity-lifts-and-bounded-treewidth-witnesses-for-Weisfeiler-Leman-equivalence-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/133.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "133:The-complexity-of-identifying-a-graph-by-Weisfeiler-Leman-refinement-September-25-2026",
      "family_id": "133",
      "discipline": "Theoretical computer science",
      "title": "The complexity of identifying a graph by Weisfeiler\u2013Leman refinement",
      "pdf_path": "preprints/The-complexity-of-identifying-a-graph-by-Weisfeiler-Leman-refinement-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-complexity-of-identifying-a-graph-by-Weisfeiler-Leman-refinement-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/133.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "133:Unconditional-time-lower-bounds-for-Weisfeiler-Leman-equivalence-September-25-2026",
      "family_id": "133",
      "discipline": "Theoretical computer science",
      "title": "Unconditional time lower bounds for Weisfeiler\u2013Leman equivalence",
      "pdf_path": "preprints/Unconditional-time-lower-bounds-for-Weisfeiler-Leman-equivalence-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unconditional-time-lower-bounds-for-Weisfeiler-Leman-equivalence-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/133.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "133:Variable-dimension-Weisfeiler-Leman-equivalence-on-general-and-subcubic-graphs-September-25-2026",
      "family_id": "133",
      "discipline": "Theoretical computer science",
      "title": "Variable-dimension Weisfeiler\u2013Leman equivalence on general and subcubic graphs",
      "pdf_path": "preprints/Variable-dimension-Weisfeiler-Leman-equivalence-on-general-and-subcubic-graphs-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Variable-dimension-Weisfeiler-Leman-equivalence-on-general-and-subcubic-graphs-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/133.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "134:Finite-Monoid-Computations-and-a-Uniform-Generalized-Star-Height-Bound-September-25-2026",
      "family_id": "134",
      "discipline": "Theoretical computer science",
      "title": "Finite Monoid Computations and a Uniform Generalized Star-Height Bound",
      "pdf_path": "preprints/Finite-Monoid-Computations-and-a-Uniform-Generalized-Star-Height-Bound-September-25-2026/Finite-Monoid-Computations-and-a-Uniform-Generalized-Star-Height-Bound-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-Monoid-Computations-and-a-Uniform-Generalized-Star-Height-Bound-September-25-2026/Finite-Monoid-Computations-and-a-Uniform-Generalized-Star-Height-Bound-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/134.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "134:Generalized-Star-Height-at-Most-Four-September-25-2026",
      "family_id": "134",
      "discipline": "Theoretical computer science",
      "title": "Generalized Star Height at Most Four",
      "pdf_path": "preprints/Generalized-Star-Height-at-Most-Four-September-25-2026/Generalized-Star-Height-at-Most-Four-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Generalized-Star-Height-at-Most-Four-September-25-2026/Generalized-Star-Height-at-Most-Four-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/134.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "134:Generalized-Star-Height-at-Most-Three-September-25-2026",
      "family_id": "134",
      "discipline": "Theoretical computer science",
      "title": "Generalized Star Height at Most Three",
      "pdf_path": "preprints/Generalized-Star-Height-at-Most-Three-September-25-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Generalized-Star-Height-at-Most-Three-September-25-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/134.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "135:Homogeneous-depth-five-lower-bounds-for-iterated-matrix-multiplication-September-25-2026",
      "family_id": "135",
      "discipline": "Theoretical computer science",
      "title": "Homogeneous depth-five lower bounds for iterated matrix multiplication",
      "pdf_path": "preprints/Homogeneous-depth-five-lower-bounds-for-iterated-matrix-multiplication-September-25-2026/Homogeneous-depth-five-lower-bounds-for-iterated-matrix-multiplication-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Homogeneous-depth-five-lower-bounds-for-iterated-matrix-multiplication-September-25-2026/Homogeneous-depth-five-lower-bounds-for-iterated-matrix-multiplication-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/135.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "136:The-PCP-for-PPAD-conjecture-a-quasilinear-reduction-September-25-2026",
      "family_id": "136",
      "discipline": "Theoretical computer science",
      "title": "The PCP-for-PPAD conjecture: a quasilinear reduction",
      "pdf_path": "preprints/The-PCP-for-PPAD-conjecture-a-quasilinear-reduction-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-PCP-for-PPAD-conjecture-a-quasilinear-reduction-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "137:Simulating-One-Tape-Time-in-Two-Fifths-Power-Space-September-25-2026",
      "family_id": "137",
      "discipline": "Theoretical computer science",
      "title": "Simulating One-Tape Time in Two-Fifths-Power Space",
      "pdf_path": "preprints/Simulating-One-Tape-Time-in-Two-Fifths-Power-Space-September-25-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Simulating-One-Tape-Time-in-Two-Fifths-Power-Space-September-25-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/137.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "138:Subset-Sum-in-Time-2-power-0-49n-October-4-2026",
      "family_id": "138",
      "discipline": "Theoretical computer science",
      "title": "Subset Sum in Time $`O(2^{0.49n})`$ ",
      "pdf_path": "preprints/Subset-Sum-in-Time-2-power-0-49n-October-4-2026/subset-sum.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Subset-Sum-in-Time-2-power-0-49n-October-4-2026/subset-sum.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Subset-Sum-in-Time-2-power-0-49n-October-4-2026/build/sections/introduction.tex",
          "extent": "entire 234-line source file",
          "sha256": "583a20059e520cff2aa5d99c5c7a457da6d6deae83a664813cc2b474a1920376",
          "note": "Model/resource/error/main guard or selected certificate text read; full proof/numerical closure and source execution remain uncompleted."
        },
        {
          "path": "preprints/Subset-Sum-in-Time-2-power-0-49n-October-4-2026/build/sections/setup.tex",
          "extent": "entire 252-line source file",
          "sha256": "7a5681c2a0ec43838737d517978a49d6b2d68125f6419526a00d053a283c00ba",
          "note": "Model/resource/error/main guard or selected certificate text read; full proof/numerical closure and source execution remain uncompleted."
        },
        {
          "path": "preprints/Subset-Sum-in-Time-2-power-0-49n-October-4-2026/build/sections/implementation.tex",
          "extent": "entire 344-line source file",
          "sha256": "ef78713f1e782ccb8c0360aa2ff68e0145cef9105371423e2617215d0d6e3aea",
          "note": "Model/resource/error/main guard or selected certificate text read; full proof/numerical closure and source execution remain uncompleted."
        },
        {
          "path": "preprints/Subset-Sum-in-Time-2-power-0-49n-October-4-2026/build/sections/numerical.tex",
          "extent": "lines 1\u201365 only of a 355-line source file",
          "sha256": "a4cc12248568d90368197466f562944f119b8f68535f72c576dd2f342b33b6dd",
          "note": "Model/resource/error/main guard or selected certificate text read; full proof/numerical closure and source execution remain uncompleted."
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "138:A-Low-Space-Algorithm-for-Worst-Case-Subset-Sum-September-26-2026",
      "family_id": "138",
      "discipline": "Theoretical computer science",
      "title": "A Low-Space Algorithm for Worst-Case Subset Sum",
      "pdf_path": "preprints/A-Low-Space-Algorithm-for-Worst-Case-Subset-Sum-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Low-Space-Algorithm-for-Worst-Case-Subset-Sum-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/A-Low-Space-Algorithm-for-Worst-Case-Subset-Sum-September-26-2026/build/introduction.tex",
          "extent": "entire 227-line source file",
          "sha256": "36be7da587a332a23246d5ca9c19a4ed9f855886481fba44c10780a5710450aa",
          "note": "Model/resource/error/main guard or selected certificate text read; full proof/numerical closure and source execution remain uncompleted."
        },
        {
          "path": "preprints/A-Low-Space-Algorithm-for-Worst-Case-Subset-Sum-September-26-2026/build/implementation.tex",
          "extent": "entire 270-line source file",
          "sha256": "430e40ff767cfa5b625d46d71cdc7f90d3c8b6d9637592a07f3d9dc4c6e5870a",
          "note": "Model/resource/error/main guard or selected certificate text read; full proof/numerical closure and source execution remain uncompleted."
        },
        {
          "path": "preprints/A-Low-Space-Algorithm-for-Worst-Case-Subset-Sum-September-26-2026/build/preliminaries.tex",
          "extent": "lines 1\u201370 only of a 222-line source file",
          "sha256": "4f6f10c62224630b5582a5f187966d9b5c0273e8c3d965cf0d36934ac26e1a8f",
          "note": "Model/resource/error/main guard or selected certificate text read; full proof/numerical closure and source execution remain uncompleted."
        },
        {
          "path": "preprints/A-Low-Space-Algorithm-for-Worst-Case-Subset-Sum-September-26-2026/build/resources.tex",
          "extent": "entire 272-line source file",
          "sha256": "2b7555941f4d16098c84550f9e6069461027835f855f08d2f96db6b3c9a46b30",
          "note": "Model/resource/error/main guard or selected certificate text read; full proof/numerical closure and source execution remain uncompleted."
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "139:Subpolynomial-query-complexity-for-well-conditioned-log-concave-sampling-September-26-2026",
      "family_id": "139",
      "discipline": "Theoretical computer science",
      "title": "Subpolynomial query complexity for well-conditioned log-concave sampling",
      "pdf_path": "preprints/Subpolynomial-query-complexity-for-well-conditioned-log-concave-sampling-September-26-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Subpolynomial-query-complexity-for-well-conditioned-log-concave-sampling-September-26-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/139.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "140:Memory-and-precision-in-noiseless-Gaussian-regression-September-27-2026",
      "family_id": "140",
      "discipline": "Theoretical computer science",
      "title": "Memory and precision in noiseless Gaussian regression",
      "pdf_path": "preprints/Memory-and-precision-in-noiseless-Gaussian-regression-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Memory-and-precision-in-noiseless-Gaussian-regression-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/140.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "140:Posterior-replicas-and-conditional-information-in-Gaussian-regression-September-27-2026",
      "family_id": "140",
      "discipline": "Theoretical computer science",
      "title": "Posterior replicas and conditional information in Gaussian regression",
      "pdf_path": "preprints/Posterior-replicas-and-conditional-information-in-Gaussian-regression-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Posterior-replicas-and-conditional-information-in-Gaussian-regression-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/140.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "140:Localization-costs-and-information-growth-for-exact-Gaussian-observations-September-27-2026",
      "family_id": "140",
      "discipline": "Theoretical computer science",
      "title": "Localization costs and information growth for exact Gaussian observations",
      "pdf_path": "preprints/Localization-costs-and-information-growth-for-exact-Gaussian-observations-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Localization-costs-and-information-growth-for-exact-Gaussian-observations-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/140.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "140:Projection-moments-positive-cap-domination-and-Riesz-estimates-on-the-sphere-September-27-2026",
      "family_id": "140",
      "discipline": "Theoretical computer science",
      "title": "Projection moments, positive cap domination, and Riesz estimates on the sphere",
      "pdf_path": "preprints/Projection-moments-positive-cap-domination-and-Riesz-estimates-on-the-sphere-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Projection-moments-positive-cap-domination-and-Riesz-estimates-on-the-sphere-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/140.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "140:Replacing-Gaussian-observations-in-memory-constrained-inference-September-27-2026",
      "family_id": "140",
      "discipline": "Theoretical computer science",
      "title": "Replacing Gaussian observations in memory-constrained inference",
      "pdf_path": "preprints/Replacing-Gaussian-observations-in-memory-constrained-inference-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Replacing-Gaussian-observations-in-memory-constrained-inference-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/140.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "140:Subsphere-methods-for-memory-sample-lower-bounds-in-noiseless-Gaussian-regression-September-27-2026",
      "family_id": "140",
      "discipline": "Theoretical computer science",
      "title": "Subsphere methods for memory-sample lower bounds in noiseless Gaussian regression",
      "pdf_path": "preprints/Subsphere-methods-for-memory-sample-lower-bounds-in-noiseless-Gaussian-regression-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Subsphere-methods-for-memory-sample-lower-bounds-in-noiseless-Gaussian-regression-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/140.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "141:Existential-universal-real-sentences-in-the-counting-hierarchy-October-4-2026",
      "family_id": "141",
      "discipline": "Theoretical computer science",
      "title": "Existential\u2013universal real sentences in the counting hierarchy",
      "pdf_path": "preprints/Existential-universal-real-sentences-in-the-counting-hierarchy-October-4-2026/etr-counting-hierarchy.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Existential-universal-real-sentences-in-the-counting-hierarchy-October-4-2026/etr-counting-hierarchy.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "142:Deterministic-Polynomial-Factorization-over-Prime-Fields-October-4-2026",
      "family_id": "142",
      "discipline": "Theoretical computer science",
      "title": "Deterministic Polynomial Factorization over Prime Fields",
      "pdf_path": "preprints/Deterministic-Polynomial-Factorization-over-Prime-Fields-October-4-2026/Deterministic-Polynomial-Factorization-over-Prime-Fields.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Deterministic-Polynomial-Factorization-over-Prime-Fields-October-4-2026/Deterministic-Polynomial-Factorization-over-Prime-Fields.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "143:uniform-bounds-for-planar-polynomial-limit-cycles-September-24-2026",
      "family_id": "143",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Uniform bounds for planar polynomial limit cycles",
      "pdf_path": "preprints/uniform-bounds-for-planar-polynomial-limit-cycles-September-24-2026/uniform-bounds-for-planar-polynomial-limit-cycles-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/uniform-bounds-for-planar-polynomial-limit-cycles-September-24-2026/uniform-bounds-for-planar-polynomial-limit-cycles-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/143.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "143:two-limit-cycles-for-quintic-lienard-systems-September-24-2026",
      "family_id": "143",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Two limit cycles for quintic Li\u00e9nard systems",
      "pdf_path": "preprints/two-limit-cycles-for-quintic-lienard-systems-September-24-2026/two-limit-cycles-for-quintic-lienard-systems-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/two-limit-cycles-for-quintic-lienard-systems-September-24-2026/two-limit-cycles-for-quintic-lienard-systems-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/143.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "144:A-smooth-three-torus-diffeomorphism-with-simple-Lebesgue-spectrum-September-23-2026",
      "family_id": "144",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "A smooth three-torus diffeomorphism with simple Lebesgue spectrum",
      "pdf_path": "preprints/A-smooth-three-torus-diffeomorphism-with-simple-Lebesgue-spectrum-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-smooth-three-torus-diffeomorphism-with-simple-Lebesgue-spectrum-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/144.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "145:Rokhlins-multiple-mixing-problem-for-one-transformation-September-23-2026",
      "family_id": "145",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Rokhlin's multiple-mixing problem for one transformation",
      "pdf_path": "preprints/Rokhlins-multiple-mixing-problem-for-one-transformation-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Rokhlins-multiple-mixing-problem-for-one-transformation-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Rokhlins-multiple-mixing-problem-for-one-transformation-September-23-2026/build/sections/01-introduction.tex",
          "extent": "entire 194-line introduction",
          "note": "One invertible measure-preserving probability action, ordinary-to-all-order asymptotic implication, single-generator scope and no selected rate.",
          "sha256": "88914bccc2fac68b930898a6a5587287ad07d0be7fbec9423931f8f71ddea35a"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/145.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "146:Positive-Metric-Entropy-for-the-Standard-Map-at-Large-Parameters-September-23-2026",
      "family_id": "146",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Positive Metric Entropy for the Standard Map at Large Parameters",
      "pdf_path": "preprints/Positive-Metric-Entropy-for-the-Standard-Map-at-Large-Parameters-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Positive-Metric-Entropy-for-the-Standard-Map-at-Large-Parameters-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/146.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "147:Continuous-Phase-Foliations-Create-Analytic-Caustic-Collars-September-24-2026",
      "family_id": "147",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Continuous Phase Foliations Create Analytic Caustic Collars",
      "pdf_path": "preprints/Continuous-Phase-Foliations-Create-Analytic-Caustic-Collars-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Continuous-Phase-Foliations-Create-Analytic-Caustic-Collars-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "147:Rigidity-of-Smooth-Billiards-with-a-Continuous-Caustic-Collar-September-24-2026",
      "family_id": "147",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Rigidity of Smooth Billiards with a Continuous Caustic Collar",
      "pdf_path": "preprints/Rigidity-of-Smooth-Billiards-with-a-Continuous-Caustic-Collar-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Rigidity-of-Smooth-Billiards-with-a-Continuous-Caustic-Collar-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "148:The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026",
      "family_id": "148",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "The entropy-rate dimension formula for self-similar measures on the line",
      "pdf_path": "preprints/The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/148.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "149:Uniform-Permanence-in-Weakly-Reversible-Mass-Action-Systems-October-5-2026",
      "family_id": "149",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Uniform Permanence in Weakly Reversible Mass-Action Systems",
      "pdf_path": "preprints/Uniform-Permanence-in-Weakly-Reversible-Mass-Action-Systems-October-5-2026/permanence.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-Permanence-in-Weakly-Reversible-Mass-Action-Systems-October-5-2026/permanence.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/149.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "149:Boundedness-and-persistence-of-weakly-reversible-mass-action-systems-September-25-2026",
      "family_id": "149",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Boundedness and persistence of weakly reversible mass-action systems",
      "pdf_path": "preprints/Boundedness-and-persistence-of-weakly-reversible-mass-action-systems-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Boundedness-and-persistence-of-weakly-reversible-mass-action-systems-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/149.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "150:Weak-mixing-of-triangular-billiards-with-an-irrational-angle-October-5-2026",
      "family_id": "150",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Weak mixing of triangular billiards with an irrational angle",
      "pdf_path": "preprints/Weak-mixing-of-triangular-billiards-with-an-irrational-angle-October-5-2026/weak-mixing-triangular-billiards.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weak-mixing-of-triangular-billiards-with-an-irrational-angle-October-5-2026/weak-mixing-triangular-billiards.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/150.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "150:Ergodicity-of-triangular-billiards-with-an-irrational-angle-September-25-2026",
      "family_id": "150",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Ergodicity of triangular billiards with an irrational angle",
      "pdf_path": "preprints/Ergodicity-of-triangular-billiards-with-an-irrational-angle-September-25-2026/Ergodicity-of-triangular-billiards-with-an-irrational-angle-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Ergodicity-of-triangular-billiards-with-an-irrational-angle-September-25-2026/Ergodicity-of-triangular-billiards-with-an-irrational-angle-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/150.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "151:A-C1-Counterexample-to-the-Entropy-Conjecture-September-25-2026",
      "family_id": "151",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "A C^1 Counterexample to the Entropy Conjecture",
      "pdf_path": "preprints/A-C1-Counterexample-to-the-Entropy-Conjecture-September-25-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-C1-Counterexample-to-the-Entropy-Conjecture-September-25-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/151.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "152:A-finite-entropy-system-without-a-smooth-positive-volume-model-September-25-2026",
      "family_id": "152",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "A zero-entropy system without a smooth positive-volume model",
      "pdf_path": "preprints/A-finite-entropy-system-without-a-smooth-positive-volume-model-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-finite-entropy-system-without-a-smooth-positive-volume-model-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/152.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "153:Arithmetic-classification-and-non-Pisot-singularity-for-Bernoulli-convolutions-October-3-2026",
      "family_id": "153",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Arithmetic classification and non-Pisot singularity for Bernoulli convolutions",
      "pdf_path": "preprints/Arithmetic-classification-and-non-Pisot-singularity-for-Bernoulli-convolutions-October-3-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Arithmetic-classification-and-non-Pisot-singularity-for-Bernoulli-convolutions-October-3-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "154:Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026",
      "family_id": "154",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Pointwise Multiple Ergodic Averages for Mixing Transformations",
      "pdf_path": "preprints/Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026/multiple-ergodic-averages.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026/multiple-ergodic-averages.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "154:Pointwise-convergence-of-fourfold-ergodic-averages-for-mixing-transformations-October-4-2026",
      "family_id": "154",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Pointwise convergence of fourfold ergodic averages for mixing transformations",
      "pdf_path": "preprints/Pointwise-convergence-of-fourfold-ergodic-averages-for-mixing-transformations-October-4-2026/fourfold-ergodic-averages.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Pointwise-convergence-of-fourfold-ergodic-averages-for-mixing-transformations-October-4-2026/fourfold-ergodic-averages.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "154:Triple-ergodic-averages-with-distinct-integer-slopes-October-4-2026",
      "family_id": "154",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Triple ergodic averages with distinct integer slopes",
      "pdf_path": "preprints/Triple-ergodic-averages-with-distinct-integer-slopes-October-4-2026/triple-ergodic-distinct-slopes.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Triple-ergodic-averages-with-distinct-integer-slopes-October-4-2026/triple-ergodic-distinct-slopes.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "154:Pointwise-convergence-of-triple-ergodic-averages-for-mixing-transformations-October-4-2026",
      "family_id": "154",
      "discipline": "Dynamical systems and ergodic theory",
      "title": "Pointwise convergence of triple ergodic averages for mixing transformations",
      "pdf_path": "preprints/Pointwise-convergence-of-triple-ergodic-averages-for-mixing-transformations-October-4-2026/pointwise-triple-ergodic-averages-mixing-transformations.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Pointwise-convergence-of-triple-ergodic-averages-for-mixing-transformations-October-4-2026/pointwise-triple-ergodic-averages-mixing-transformations.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "155:A-translational-tile-with-no-fully-periodic-tiling-in-dimension-three-September-23-2026",
      "family_id": "155",
      "discipline": "Combinatorics",
      "title": "A translational tile with no fully periodic tiling in dimension three",
      "pdf_path": "preprints/A-translational-tile-with-no-fully-periodic-tiling-in-dimension-three-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-translational-tile-with-no-fully-periodic-tiling-in-dimension-three-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/155.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "156:A-nine-dimensional-counterexample-to-Borsuks-covering-assertion-September-23-2026",
      "family_id": "156",
      "discipline": "Combinatorics",
      "title": "A nine-dimensional counterexample to Borsuk's covering assertion",
      "pdf_path": "preprints/A-nine-dimensional-counterexample-to-Borsuks-covering-assertion-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-nine-dimensional-counterexample-to-Borsuks-covering-assertion-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/156.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "157:A-counterexample-to-Hadwigers-conjecture-September-23-2026",
      "family_id": "157",
      "discipline": "Combinatorics",
      "title": "A counterexample to Hadwiger's conjecture",
      "pdf_path": "preprints/A-counterexample-to-Hadwigers-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-counterexample-to-Hadwigers-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/157.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "157:A-counterexample-to-the-Colin-de-Verdiere-chromatic-conjecture-September-23-2026",
      "family_id": "157",
      "discipline": "Combinatorics",
      "title": "A counterexample to the Colin de Verdi\u00e8re chromatic conjecture",
      "pdf_path": "preprints/A-counterexample-to-the-Colin-de-Verdiere-chromatic-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-counterexample-to-the-Colin-de-Verdiere-chromatic-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/157.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "157:A-linear-list-coloring-bound-in-terms-of-the-Hadwiger-number-September-23-2026",
      "family_id": "157",
      "discipline": "Combinatorics",
      "title": "A linear list-coloring bound in terms of the Hadwiger number",
      "pdf_path": "preprints/A-linear-list-coloring-bound-in-terms-of-the-Hadwiger-number-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-linear-list-coloring-bound-in-terms-of-the-Hadwiger-number-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/157.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "158:The-Euclidean-plane-is-not-five-colorable-September-23-2026",
      "family_id": "158",
      "discipline": "Combinatorics",
      "title": "The Euclidean plane is not five-colorable",
      "pdf_path": "preprints/The-Euclidean-plane-is-not-five-colorable-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Euclidean-plane-is-not-five-colorable-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/The-Euclidean-plane-is-not-five-colorable-September-23-2026/build/sections/introduction.tex",
          "extent": "entire 324-line introduction",
          "note": "Claimed six-to-seven chromatic range, continuum obstruction, proper/weak-measurable distinction, compactness existence without an explicit finite six-required graph, selected hexagonal upper bound.",
          "sha256": "41222c5b4e8be3352a08fa554116285007268c841216432fa8aab62208a96e1a"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/158.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "159:Quasipolynomial-Bounds-for-Arithmetic-Progressions-September-23-2026",
      "family_id": "159",
      "discipline": "Combinatorics",
      "title": "Quasipolynomial Bounds for Arithmetic Progressions",
      "pdf_path": "preprints/Quasipolynomial-Bounds-for-Arithmetic-Progressions-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Quasipolynomial-Bounds-for-Arithmetic-Progressions-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/159.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "160:Quantitative-Superexponential-Bounds-for-van-der-Waerden-Numbers-September-23-2026",
      "family_id": "160",
      "discipline": "Combinatorics",
      "title": "Quantitative Superexponential Bounds for van der Waerden Numbers",
      "pdf_path": "preprints/Quantitative-Superexponential-Bounds-for-van-der-Waerden-Numbers-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Quantitative-Superexponential-Bounds-for-van-der-Waerden-Numbers-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/160.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "161:A-counterexample-to-Sidorenkos-conjecture-September-23-2026",
      "family_id": "161",
      "discipline": "Combinatorics",
      "title": "A counterexample to Sidorenko's conjecture",
      "pdf_path": "preprints/A-counterexample-to-Sidorenkos-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-counterexample-to-Sidorenkos-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/161.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "162:Balanced-Counterexamples-to-Rysers-Conjecture-at-Prime-Orders-September-27-2026",
      "family_id": "162",
      "discipline": "Combinatorics",
      "title": "Balanced counterexamples to Ryser's conjecture at prime orders",
      "pdf_path": "preprints/Balanced-Counterexamples-to-Rysers-Conjecture-at-Prime-Orders-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Balanced-Counterexamples-to-Rysers-Conjecture-at-Prime-Orders-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/162.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "162:A-Counterexample-to-Rysers-Covering-Conjecture-September-23-2026",
      "family_id": "162",
      "discipline": "Combinatorics",
      "title": "A counterexample to Ryser's covering conjecture",
      "pdf_path": "preprints/A-Counterexample-to-Rysers-Covering-Conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Counterexample-to-Rysers-Covering-Conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/162.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "164:Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026",
      "family_id": "164",
      "discipline": "Combinatorics",
      "title": "Monochromatic finite sums and products in the positive integers",
      "pdf_path": "preprints/Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "165:The-crossing-number-of-complete-graphs-September-23-2026",
      "family_id": "165",
      "discipline": "Combinatorics",
      "title": "The crossing number of complete graphs",
      "pdf_path": "preprints/The-crossing-number-of-complete-graphs-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-crossing-number-of-complete-graphs-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/165.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "165:The-crossing-number-of-complete-bipartite-graphs-September-23-2026",
      "family_id": "165",
      "discipline": "Combinatorics",
      "title": "The crossing number of complete bipartite graphs",
      "pdf_path": "preprints/The-crossing-number-of-complete-bipartite-graphs-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-crossing-number-of-complete-bipartite-graphs-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/165.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "166:The-higher-dimensional-Erdos-distinct-distances-conjecture-September-23-2026",
      "family_id": "166",
      "discipline": "Combinatorics",
      "title": "The higher-dimensional Erd\u0151s distinct-distances conjecture",
      "pdf_path": "preprints/The-higher-dimensional-Erdos-distinct-distances-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-higher-dimensional-Erdos-distinct-distances-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "167:The-weak-pinned-planar-distance-theorem-September-23-2026",
      "family_id": "167",
      "discipline": "Combinatorics",
      "title": "The weak pinned planar distance theorem",
      "pdf_path": "preprints/The-weak-pinned-planar-distance-theorem-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-weak-pinned-planar-distance-theorem-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/167.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "167:A-power-saving-for-planar-unit-distances-September-23-2026",
      "family_id": "167",
      "discipline": "Combinatorics",
      "title": "A power saving for planar unit distances",
      "pdf_path": "preprints/A-power-saving-for-planar-unit-distances-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-power-saving-for-planar-unit-distances-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/167.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "168:Combinatorial-Invariance-of-Kazhdan-Lusztig-Polynomials-September-24-2026",
      "family_id": "168",
      "discipline": "Combinatorics",
      "title": "Combinatorial invariance of Kazhdan\u2013Lusztig polynomials",
      "pdf_path": "preprints/Combinatorial-Invariance-of-Kazhdan-Lusztig-Polynomials-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Combinatorial-Invariance-of-Kazhdan-Lusztig-Polynomials-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/168.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "169:Elementary-Positivity-of-Chromatic-Quasisymmetric-Functions-September-24-2026",
      "family_id": "169",
      "discipline": "Combinatorics",
      "title": "Elementary positivity of chromatic quasisymmetric functions",
      "pdf_path": "preprints/Elementary-Positivity-of-Chromatic-Quasisymmetric-Functions-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Elementary-Positivity-of-Chromatic-Quasisymmetric-Functions-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Elementary-Positivity-of-Chromatic-Quasisymmetric-Functions-September-24-2026/build/sections/01-introduction.tex",
          "extent": "entire 312-line introduction",
          "note": "Natural unit interval graph elementary positivity, individual witness and terminating finite procedure; no time efficiency or elementary unimodality claim.",
          "sha256": "10e0c45e1bb975155096768fd77d3d93da69bc4f9d28993d72da03363ed7e64a"
        },
        {
          "path": "preprints/Elementary-Positivity-of-Chromatic-Quasisymmetric-Functions-September-24-2026/build/sections/06-witness.tex",
          "extent": "lines 1\u2013130 and 560\u2013629",
          "note": "Finite-cone/root packet setup and selected history/algorithm/consequence passage; middle proof not reviewed.",
          "sha256": "8ef0cd77af2b084746f2be648cb4b92459c6d9b4061c49302c92ccd11feac9c8"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/169.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "170:The-Sharp-Logarithmic-Exponent-of-r-5-t-September-24-2026",
      "family_id": "170",
      "discipline": "Combinatorics",
      "title": "The sharp logarithmic exponent of r(5,t)",
      "pdf_path": "preprints/The-Sharp-Logarithmic-Exponent-of-r-5-t-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Sharp-Logarithmic-Exponent-of-r-5-t-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/170.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "170:Sharp-Logarithmic-Exponents-for-Fixed-Off-Diagonal-Ramsey-Numbers-September-24-2026",
      "family_id": "170",
      "discipline": "Combinatorics",
      "title": "Sharp logarithmic exponents for fixed off-diagonal Ramsey numbers",
      "pdf_path": "preprints/Sharp-Logarithmic-Exponents-for-Fixed-Off-Diagonal-Ramsey-Numbers-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Sharp-Logarithmic-Exponents-for-Fixed-Off-Diagonal-Ramsey-Numbers-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/170.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "171:The-hypercube-Ramsey-number-has-linear-order-September-23-2026",
      "family_id": "171",
      "discipline": "Combinatorics",
      "title": "The hypercube Ramsey number has linear order",
      "pdf_path": "preprints/The-hypercube-Ramsey-number-has-linear-order-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-hypercube-Ramsey-number-has-linear-order-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "172:A-classification-of-finite-Euclidean-Ramsey-configurations-September-23-2026",
      "family_id": "172",
      "discipline": "Combinatorics",
      "title": "A classification of finite Euclidean Ramsey configurations",
      "pdf_path": "preprints/A-classification-of-finite-Euclidean-Ramsey-configurations-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-classification-of-finite-Euclidean-Ramsey-configurations-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/172.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "173:A-proof-of-Seymours-second-neighborhood-conjecture-September-23-2026",
      "family_id": "173",
      "discipline": "Combinatorics",
      "title": "A proof of Seymour\u2019s second-neighborhood conjecture",
      "pdf_path": "preprints/A-proof-of-Seymours-second-neighborhood-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-proof-of-Seymours-second-neighborhood-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/173.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "174:The-strong-thin-tree-conjecture-September-23-2026",
      "family_id": "174",
      "discipline": "Combinatorics",
      "title": "The strong thin tree conjecture",
      "pdf_path": "preprints/The-strong-thin-tree-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-strong-thin-tree-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/The-strong-thin-tree-conjecture-September-23-2026/build/source/sections/introduction.tex",
          "extent": "full existence introduction",
          "note": "Read the existence introduction, constructive introduction/main theorem, iteration/binary reduction and fractional cost/cut rounding; selected signing statement/constant and formal scope were also read. The existence fixed-point step does not itself supply the finite construction. With stated Cs=2^20, the declared cut factor certifies strict contraction only above r=(6Cs)^8, a 55-digit quantity. This is not a final C, input/runtime lower bound or impossibility. R0 and final C are not numerically selected. The cost corollary uses nonnegative rational inputs and an all-cut fractional promise; it is not separately listed in the selected family scope. The bounded exact auditor shows K4 path fundamental-cut ratio 1/3 versus true all-cut ratio 3/4. It is exponential finite validation, not the polynomial source constructor or routing/redundancy evidence. Dossier 024 is revised.",
          "sha256": "fc32e6c483da6b2f940842a98b6a1e59602f220ae305af8cc5a4442116745ec4"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/174.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "174:A-polynomial-time-construction-of-strong-thin-trees-September-23-2026",
      "family_id": "174",
      "discipline": "Combinatorics",
      "title": "A polynomial-time construction of strong thin trees",
      "pdf_path": "preprints/A-polynomial-time-construction-of-strong-thin-trees-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-polynomial-time-construction-of-strong-thin-trees-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/A-polynomial-time-construction-of-strong-thin-trees-September-23-2026/build/source/sections/introduction.tex",
          "extent": "full constructive introduction",
          "note": "Read the existence introduction, constructive introduction/main theorem, iteration/binary reduction and fractional cost/cut rounding; selected signing statement/constant and formal scope were also read. The existence fixed-point step does not itself supply the finite construction. With stated Cs=2^20, the declared cut factor certifies strict contraction only above r=(6Cs)^8, a 55-digit quantity. This is not a final C, input/runtime lower bound or impossibility. R0 and final C are not numerically selected. The cost corollary uses nonnegative rational inputs and an all-cut fractional promise; it is not separately listed in the selected family scope. The bounded exact auditor shows K4 path fundamental-cut ratio 1/3 versus true all-cut ratio 3/4. It is exponential finite validation, not the polynomial source constructor or routing/redundancy evidence. Dossier 024 is revised.",
          "sha256": "feda19d4f085b7fb99836300656c3f520c6db71089807d175d3d207bb4b4005e"
        },
        {
          "path": "preprints/A-polynomial-time-construction-of-strong-thin-trees-September-23-2026/build/source/sections/main-theorem.tex",
          "extent": "full main statement",
          "note": "Read the existence introduction, constructive introduction/main theorem, iteration/binary reduction and fractional cost/cut rounding; selected signing statement/constant and formal scope were also read. The existence fixed-point step does not itself supply the finite construction. With stated Cs=2^20, the declared cut factor certifies strict contraction only above r=(6Cs)^8, a 55-digit quantity. This is not a final C, input/runtime lower bound or impossibility. R0 and final C are not numerically selected. The cost corollary uses nonnegative rational inputs and an all-cut fractional promise; it is not separately listed in the selected family scope. The bounded exact auditor shows K4 path fundamental-cut ratio 1/3 versus true all-cut ratio 3/4. It is exponential finite validation, not the polynomial source constructor or routing/redundancy evidence. Dossier 024 is revised.",
          "sha256": "b5f49f7407fc14ad8677b4f54bf429192b1326e8b5d87237c9ca6d5003a0a94a"
        },
        {
          "path": "preprints/A-polynomial-time-construction-of-strong-thin-trees-September-23-2026/build/source/sections/iteration.tex",
          "extent": "full iteration/binary reduction",
          "note": "Read the existence introduction, constructive introduction/main theorem, iteration/binary reduction and fractional cost/cut rounding; selected signing statement/constant and formal scope were also read. The existence fixed-point step does not itself supply the finite construction. With stated Cs=2^20, the declared cut factor certifies strict contraction only above r=(6Cs)^8, a 55-digit quantity. This is not a final C, input/runtime lower bound or impossibility. R0 and final C are not numerically selected. The cost corollary uses nonnegative rational inputs and an all-cut fractional promise; it is not separately listed in the selected family scope. The bounded exact auditor shows K4 path fundamental-cut ratio 1/3 versus true all-cut ratio 3/4. It is exponential finite validation, not the polynomial source constructor or routing/redundancy evidence. Dossier 024 is revised.",
          "sha256": "3be9281b79efd0d516965eb0ef473be98abcf0e6b7a7075f61fd88689114eb61"
        },
        {
          "path": "preprints/A-polynomial-time-construction-of-strong-thin-trees-September-23-2026/build/source/sections/fractional_rounding.tex",
          "extent": "full cost/cut rounding section",
          "note": "Read the existence introduction, constructive introduction/main theorem, iteration/binary reduction and fractional cost/cut rounding; selected signing statement/constant and formal scope were also read. The existence fixed-point step does not itself supply the finite construction. With stated Cs=2^20, the declared cut factor certifies strict contraction only above r=(6Cs)^8, a 55-digit quantity. This is not a final C, input/runtime lower bound or impossibility. R0 and final C are not numerically selected. The cost corollary uses nonnegative rational inputs and an all-cut fractional promise; it is not separately listed in the selected family scope. The bounded exact auditor shows K4 path fundamental-cut ratio 1/3 versus true all-cut ratio 3/4. It is exponential finite validation, not the polynomial source constructor or routing/redundancy evidence. Dossier 024 is revised.",
          "sha256": "e6bd1cc8baf230202cd71473eb1f3a77a4be100c3747cb7648abe6c153eae532"
        },
        {
          "path": "preprints/A-polynomial-time-construction-of-strong-thin-trees-September-23-2026/build/source/sections/signing.tex",
          "extent": "lines 73\u2013100 and 180\u2013207",
          "note": "Read the existence introduction, constructive introduction/main theorem, iteration/binary reduction and fractional cost/cut rounding; selected signing statement/constant and formal scope were also read. The existence fixed-point step does not itself supply the finite construction. With stated Cs=2^20, the declared cut factor certifies strict contraction only above r=(6Cs)^8, a 55-digit quantity. This is not a final C, input/runtime lower bound or impossibility. R0 and final C are not numerically selected. The cost corollary uses nonnegative rational inputs and an all-cut fractional promise; it is not separately listed in the selected family scope. The bounded exact auditor shows K4 path fundamental-cut ratio 1/3 versus true all-cut ratio 3/4. It is exponential finite validation, not the polynomial source constructor or routing/redundancy evidence. Dossier 024 is revised.",
          "sha256": "d4e06588b924fc04a2f0886086ee280b37b22f0aa01d6d9184c3ca47fbea804a"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/174.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "175:Graph-Decompositions-at-the-Integral-Expectation-Threshold-October-5-2026",
      "family_id": "175",
      "discipline": "Combinatorics",
      "title": "Graph Decompositions at the Integral Expectation Threshold",
      "pdf_path": "preprints/Graph-Decompositions-at-the-Integral-Expectation-Threshold-October-5-2026/graph-threshold-decompositions.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Graph-Decompositions-at-the-Integral-Expectation-Threshold-October-5-2026/graph-threshold-decompositions.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/175.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "175:Integral-and-fractional-expectation-thresholds-are-equivalent-September-23-2026",
      "family_id": "175",
      "discipline": "Combinatorics",
      "title": "Integral and fractional expectation thresholds are equivalent",
      "pdf_path": "preprints/Integral-and-fractional-expectation-thresholds-are-equivalent-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Integral-and-fractional-expectation-thresholds-are-equivalent-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/175.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "175:Talagrands-discrete-convexity-conjecture-September-23-2026",
      "family_id": "175",
      "discipline": "Combinatorics",
      "title": "Talagrand\u2019s discrete-convexity conjecture",
      "pdf_path": "preprints/Talagrands-discrete-convexity-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Talagrands-discrete-convexity-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/175.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "176:The-second-Kahn-Kalai-conjecture-September-24-2026",
      "family_id": "176",
      "discipline": "Combinatorics",
      "title": "The second Kahn\u2013Kalai conjecture",
      "pdf_path": "preprints/The-second-Kahn-Kalai-conjecture-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-second-Kahn-Kalai-conjecture-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/176.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "177:Bounded-degree-coboundary-expanders-in-every-dimension-September-24-2026",
      "family_id": "177",
      "discipline": "Combinatorics",
      "title": "Bounded-degree coboundary expanders in every dimension",
      "pdf_path": "preprints/Bounded-degree-coboundary-expanders-in-every-dimension-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Bounded-degree-coboundary-expanders-in-every-dimension-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/177.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "178:Deterministic-nonbipartite-Ramanujan-graphs-in-every-fixed-degree-September-23-2026",
      "family_id": "178",
      "discipline": "Combinatorics",
      "title": "Deterministic nonbipartite Ramanujan graphs in every fixed degree",
      "pdf_path": "preprints/Deterministic-nonbipartite-Ramanujan-graphs-in-every-fixed-degree-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Deterministic-nonbipartite-Ramanujan-graphs-in-every-fixed-degree-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Deterministic-nonbipartite-Ramanujan-graphs-in-every-fixed-degree-September-23-2026/build/sections/introduction.tex",
          "extent": "full introduction",
          "note": "Read full introduction, setup and algorithm; selected accounts, exact-repair theorem and affine seed enumeration were also read. Fixed a=1/10000 implies 3,333,334 auxiliary points and 6,666,668 signed auxiliary points during early/cleanup phases. This is a parameter count, not a moment order, complexity exponent or mandatory simultaneous-memory allocation. Repair enumerates P squared seeds with an unselected sufficiently-large fixed exponent. n0(d), kd and remaining parameter margins are not numerically instantiated. The theorem outputs an adjacency list at sufficiently large even orders for fixed degree, not joint-polynomial degree/order or local-query access. The exact finite acceptance checker remains useful independently of a full constructor. No family formal scope is listed, no independent proof check was run, and full construction/proof review remains pending. Dossier 036 is revised.",
          "sha256": "1ba28efd51ec881f8d8b8f5af8b0b17a44ea65ed5a72dc8e7778de24acc6a6e9"
        },
        {
          "path": "preprints/Deterministic-nonbipartite-Ramanujan-graphs-in-every-fixed-degree-September-23-2026/build/sections/setup.tex",
          "extent": "full parameter hierarchy",
          "note": "Read full introduction, setup and algorithm; selected accounts, exact-repair theorem and affine seed enumeration were also read. Fixed a=1/10000 implies 3,333,334 auxiliary points and 6,666,668 signed auxiliary points during early/cleanup phases. This is a parameter count, not a moment order, complexity exponent or mandatory simultaneous-memory allocation. Repair enumerates P squared seeds with an unselected sufficiently-large fixed exponent. n0(d), kd and remaining parameter margins are not numerically instantiated. The theorem outputs an adjacency list at sufficiently large even orders for fixed degree, not joint-polynomial degree/order or local-query access. The exact finite acceptance checker remains useful independently of a full constructor. No family formal scope is listed, no independent proof check was run, and full construction/proof review remains pending. Dossier 036 is revised.",
          "sha256": "ac7a38b863819f3f375ac9b8335f2ca8759aa8c6c1590f282fa45de17688a40e"
        },
        {
          "path": "preprints/Deterministic-nonbipartite-Ramanujan-graphs-in-every-fixed-degree-September-23-2026/build/sections/accounts.tex",
          "extent": "lines 1\u2013115",
          "note": "Read full introduction, setup and algorithm; selected accounts, exact-repair theorem and affine seed enumeration were also read. Fixed a=1/10000 implies 3,333,334 auxiliary points and 6,666,668 signed auxiliary points during early/cleanup phases. This is a parameter count, not a moment order, complexity exponent or mandatory simultaneous-memory allocation. Repair enumerates P squared seeds with an unselected sufficiently-large fixed exponent. n0(d), kd and remaining parameter margins are not numerically instantiated. The theorem outputs an adjacency list at sufficiently large even orders for fixed degree, not joint-polynomial degree/order or local-query access. The exact finite acceptance checker remains useful independently of a full constructor. No family formal scope is listed, no independent proof check was run, and full construction/proof review remains pending. Dossier 036 is revised.",
          "sha256": "062e3788617a1a0e08a697132c43ce50044a0d5ce6d7543f17a8c2b41a179432"
        },
        {
          "path": "preprints/Deterministic-nonbipartite-Ramanujan-graphs-in-every-fixed-degree-September-23-2026/build/sections/algorithm.tex",
          "extent": "full algorithm/bit-model section",
          "note": "Read full introduction, setup and algorithm; selected accounts, exact-repair theorem and affine seed enumeration were also read. Fixed a=1/10000 implies 3,333,334 auxiliary points and 6,666,668 signed auxiliary points during early/cleanup phases. This is a parameter count, not a moment order, complexity exponent or mandatory simultaneous-memory allocation. Repair enumerates P squared seeds with an unselected sufficiently-large fixed exponent. n0(d), kd and remaining parameter margins are not numerically instantiated. The theorem outputs an adjacency list at sufficiently large even orders for fixed degree, not joint-polynomial degree/order or local-query access. The exact finite acceptance checker remains useful independently of a full constructor. No family formal scope is listed, no independent proof check was run, and full construction/proof review remains pending. Dossier 036 is revised.",
          "sha256": "746a29c8e8a09be81f94def54b69515d2cc7158542802e793395071f5d9bfd41"
        },
        {
          "path": "preprints/Deterministic-nonbipartite-Ramanujan-graphs-in-every-fixed-degree-September-23-2026/build/sections/repair.tex",
          "extent": "lines 280\u2013335 and 724\u2013764",
          "note": "Read full introduction, setup and algorithm; selected accounts, exact-repair theorem and affine seed enumeration were also read. Fixed a=1/10000 implies 3,333,334 auxiliary points and 6,666,668 signed auxiliary points during early/cleanup phases. This is a parameter count, not a moment order, complexity exponent or mandatory simultaneous-memory allocation. Repair enumerates P squared seeds with an unselected sufficiently-large fixed exponent. n0(d), kd and remaining parameter margins are not numerically instantiated. The theorem outputs an adjacency list at sufficiently large even orders for fixed degree, not joint-polynomial degree/order or local-query access. The exact finite acceptance checker remains useful independently of a full constructor. No family formal scope is listed, no independent proof check was run, and full construction/proof review remains pending. Dossier 036 is revised.",
          "sha256": "d6a9bafdc51fa99469bea7b74f7faa8cb22a6b3e1160d9804edacbc230cd3af5"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "179:The-circulant-Hadamard-conjecture-September-23-2026",
      "family_id": "179",
      "discipline": "Combinatorics",
      "title": "The circulant Hadamard conjecture",
      "pdf_path": "preprints/The-circulant-Hadamard-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-circulant-Hadamard-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/179.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "180:Paired-states-and-Hamiltonian-cycles-in-cubic-bipartite-planar-graphs-September-24-2026",
      "family_id": "180",
      "discipline": "Combinatorics",
      "title": "Paired states and Hamiltonian cycles in cubic bipartite planar graphs",
      "pdf_path": "preprints/Paired-states-and-Hamiltonian-cycles-in-cubic-bipartite-planar-graphs-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Paired-states-and-Hamiltonian-cycles-in-cubic-bipartite-planar-graphs-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/180.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "181:A-linear-cycle-and-edge-decomposition-of-every-graph-September-24-2026",
      "family_id": "181",
      "discipline": "Combinatorics",
      "title": "A linear cycle-and-edge decomposition of every graph",
      "pdf_path": "preprints/A-linear-cycle-and-edge-decomposition-of-every-graph-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-linear-cycle-and-edge-decomposition-of-every-graph-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/181.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "182:A-power-saving-for-intersective-polynomial-differences-with-an-exponent-depending-only-on-the-degree-October-5-2026",
      "family_id": "182",
      "discipline": "Combinatorics",
      "title": "A power saving for intersective polynomial differences with an exponent depending only on the degree",
      "pdf_path": "preprints/A-power-saving-for-intersective-polynomial-differences-with-an-exponent-depending-only-on-the-degree-October-5-2026/power-saving-intersective-polynomial-differences.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-power-saving-for-intersective-polynomial-differences-with-an-exponent-depending-only-on-the-degree-October-5-2026/power-saving-intersective-polynomial-differences.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/182.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "182:A-Power-Saving-for-Polynomial-Differences-at-Prime-Arguments-October-5-2026",
      "family_id": "182",
      "discipline": "Combinatorics",
      "title": "A Power Saving for Polynomial Differences at Prime Arguments",
      "pdf_path": "preprints/A-Power-Saving-for-Polynomial-Differences-at-Prime-Arguments-October-5-2026/prime-argument-polynomial-differences.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Power-Saving-for-Polynomial-Differences-at-Prime-Arguments-October-5-2026/prime-argument-polynomial-differences.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/182.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "182:A-power-saving-for-square-difference-free-sets-September-24-2026",
      "family_id": "182",
      "discipline": "Combinatorics",
      "title": "A power saving for square-difference-free sets",
      "pdf_path": "preprints/A-power-saving-for-square-difference-free-sets-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-power-saving-for-square-difference-free-sets-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/182.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "183:A-power-saving-for-planar-halving-lines-September-25-2026",
      "family_id": "183",
      "discipline": "Combinatorics",
      "title": "A power saving for planar halving lines",
      "pdf_path": "preprints/A-power-saving-for-planar-halving-lines-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-power-saving-for-planar-halving-lines-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/183.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "184:Correspondence-Coloring-Graphs-with-a-Forbidden-Clique-October-5-2026",
      "family_id": "184",
      "discipline": "Combinatorics",
      "title": "Correspondence coloring graphs with a forbidden clique",
      "pdf_path": "preprints/Correspondence-Coloring-Graphs-with-a-Forbidden-Clique-October-5-2026/correspondence-coloring-forbidden-clique.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Correspondence-Coloring-Graphs-with-a-Forbidden-Clique-October-5-2026/correspondence-coloring-forbidden-clique.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/184.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "184:A-Logarithmic-Independence-Bound-for-Clique-Free-Graphs-September-25-2026",
      "family_id": "184",
      "discipline": "Combinatorics",
      "title": "A logarithmic independence bound for clique-free graphs",
      "pdf_path": "preprints/A-Logarithmic-Independence-Bound-for-Clique-Free-Graphs-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Logarithmic-Independence-Bound-for-Clique-Free-Graphs-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/184.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "185:A-Counterexample-to-the-Infinite-Matroid-Packing-Covering-Conjecture-September-24-2026",
      "family_id": "185",
      "discipline": "Combinatorics",
      "title": "A Counterexample to the Infinite Matroid Packing/Covering Conjecture",
      "pdf_path": "preprints/A-Counterexample-to-the-Infinite-Matroid-Packing-Covering-Conjecture-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Counterexample-to-the-Infinite-Matroid-Packing-Covering-Conjecture-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/185.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "186:A-uniform-influence-bound-for-hypergraph-properties-October-5-2026",
      "family_id": "186",
      "discipline": "Combinatorics",
      "title": "A uniform influence bound for hypergraph properties",
      "pdf_path": "preprints/A-uniform-influence-bound-for-hypergraph-properties-October-5-2026/hypergraph-influences.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-uniform-influence-bound-for-hypergraph-properties-October-5-2026/hypergraph-influences.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/186.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "186:A-Sharp-Threshold-Bound-for-Monotone-Graph-Properties-September-25-2026",
      "family_id": "186",
      "discipline": "Combinatorics",
      "title": "A Sharp Threshold Bound for Monotone Graph Properties",
      "pdf_path": "preprints/A-Sharp-Threshold-Bound-for-Monotone-Graph-Properties-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Sharp-Threshold-Bound-for-Monotone-Graph-Properties-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/186.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "187:Snaky-in-21-Maker-moves-September-25-2026",
      "family_id": "187",
      "discipline": "Combinatorics",
      "title": "Snaky in 21 Maker moves",
      "pdf_path": "preprints/Snaky-in-21-Maker-moves-September-25-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Snaky-in-21-Maker-moves-September-25-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/187.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "188:The-Sharp-Terminal-Leave-in-Random-Triangle-Removal-September-25-2026",
      "family_id": "188",
      "discipline": "Combinatorics",
      "title": "The sharp terminal leave in random triangle removal",
      "pdf_path": "preprints/The-Sharp-Terminal-Leave-in-Random-Triangle-Removal-September-25-2026/The-Sharp-Terminal-Leave-in-Random-Triangle-Removal-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Sharp-Terminal-Leave-in-Random-Triangle-Removal-September-25-2026/The-Sharp-Terminal-Leave-in-Random-Triangle-Removal-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/188.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "189:Cycle-clique-Ramsey-numbers-September-25-2026",
      "family_id": "189",
      "discipline": "Combinatorics",
      "title": "Cycle--clique Ramsey numbers",
      "pdf_path": "preprints/Cycle-clique-Ramsey-numbers-September-25-2026/Cycle-clique-Ramsey-numbers-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Cycle-clique-Ramsey-numbers-September-25-2026/Cycle-clique-Ramsey-numbers-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/189.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "190:Polynomial-removal-fails-for-ordered-binary-matrices-September-25-2026",
      "family_id": "190",
      "discipline": "Combinatorics",
      "title": "Polynomial removal fails for ordered binary matrices",
      "pdf_path": "preprints/Polynomial-removal-fails-for-ordered-binary-matrices-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Polynomial-removal-fails-for-ordered-binary-matrices-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/190.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "191:A-power-improvement-in-the-Heilbronn-triangle-lower-bound-September-25-2026",
      "family_id": "191",
      "discipline": "Combinatorics",
      "title": "A power improvement in the Heilbronn triangle lower bound",
      "pdf_path": "preprints/A-power-improvement-in-the-Heilbronn-triangle-lower-bound-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-power-improvement-in-the-Heilbronn-triangle-lower-bound-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/191.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "192:Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026",
      "family_id": "192",
      "discipline": "Combinatorics",
      "title": "Unbounded Violations of the Square-Root Degree Bound",
      "pdf_path": "preprints/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/192.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "193:Positivity-of-Serres-Intersection-Multiplicity-September-23-2026",
      "family_id": "193",
      "discipline": "Algebra",
      "title": "Positivity of Serre's Intersection Multiplicity",
      "pdf_path": "preprints/Positivity-of-Serres-Intersection-Multiplicity-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Positivity-of-Serres-Intersection-Multiplicity-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "194:Lechs-multiplicity-conjecture-September-23-2026",
      "family_id": "194",
      "discipline": "Algebra",
      "title": "Lech's multiplicity conjecture",
      "pdf_path": "preprints/Lechs-multiplicity-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Lechs-multiplicity-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/194.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "195:A-Complete-Local-Domain-Without-a-Small-Cohen-Macaulay-Module-September-23-2026",
      "family_id": "195",
      "discipline": "Algebra",
      "title": "A Complete Local Domain without a Small Cohen\u2013Macaulay Module",
      "pdf_path": "preprints/A-Complete-Local-Domain-Without-a-Small-Cohen-Macaulay-Module-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Complete-Local-Domain-Without-a-Small-Cohen-Macaulay-Module-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/195.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "196:A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026",
      "family_id": "196",
      "discipline": "Algebra",
      "title": "A Torsion-Free Group Algebra with Zero Divisors",
      "pdf_path": "preprints/A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/196.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "197:A-Torsion-Free-Group-Algebra-That-Is-Not-Directly-Finite-October-4-2026",
      "family_id": "197",
      "discipline": "Algebra",
      "title": "A Torsion-Free Group Algebra That Is Not Directly Finite",
      "pdf_path": "preprints/A-Torsion-Free-Group-Algebra-That-Is-Not-Directly-Finite-October-4-2026/direct-finiteness.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Torsion-Free-Group-Algebra-That-Is-Not-Directly-Finite-October-4-2026/direct-finiteness.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/197.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "197:A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Characteristic-Two-September-23-2026",
      "family_id": "197",
      "discipline": "Algebra",
      "title": "A Counterexample to Kaplansky's Direct-Finiteness Conjecture in Characteristic Two",
      "pdf_path": "preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Characteristic-Two-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Characteristic-Two-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/197.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "197:A-Counterexample-to-the-Group-Ring-Determinant-Conjecture-September-23-2026",
      "family_id": "197",
      "discipline": "Algebra",
      "title": "A Counterexample to the Group-Ring Determinant Conjecture",
      "pdf_path": "preprints/A-Counterexample-to-the-Group-Ring-Determinant-Conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Counterexample-to-the-Group-Ring-Determinant-Conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/197.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "197:A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Odd-Characteristic-September-26-2026",
      "family_id": "197",
      "discipline": "Algebra",
      "title": "A Counterexample to Kaplansky's Direct-Finiteness Conjecture in Odd Characteristic",
      "pdf_path": "preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Odd-Characteristic-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Odd-Characteristic-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/197.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "198:An-algebra-of-infinite-little-finitistic-dimension-September-23-2026",
      "family_id": "198",
      "discipline": "Algebra",
      "title": "An algebra of infinite little finitistic dimension",
      "pdf_path": "preprints/An-algebra-of-infinite-little-finitistic-dimension-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-algebra-of-infinite-little-finitistic-dimension-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/198.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "199:An-explicit-counterexample-to-the-Auslander-Reiten-conjecture-September-23-2026",
      "family_id": "199",
      "discipline": "Algebra",
      "title": "An explicit counterexample to the Auslander-Reiten conjecture",
      "pdf_path": "preprints/An-explicit-counterexample-to-the-Auslander-Reiten-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-explicit-counterexample-to-the-Auslander-Reiten-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/199.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "199:A-counterexample-to-Tachikawas-second-conjecture-September-23-2026",
      "family_id": "199",
      "discipline": "Algebra",
      "title": "A counterexample to Tachikawa's second conjecture",
      "pdf_path": "preprints/A-counterexample-to-Tachikawas-second-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-counterexample-to-Tachikawas-second-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/199.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "200:The-Artinian-Lex-Plus-Powers-Betti-Theorem-September-23-2026",
      "family_id": "200",
      "discipline": "Algebra",
      "title": "The Artinian Lex-Plus-Powers Betti Theorem",
      "pdf_path": "preprints/The-Artinian-Lex-Plus-Powers-Betti-Theorem-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Artinian-Lex-Plus-Powers-Betti-Theorem-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "200:Commuting-Division-Coefficient-Forms-and-the-Artinian-Eisenbud-Green-Harris-Conjecture-September-23-2026",
      "family_id": "200",
      "discipline": "Algebra",
      "title": "Commuting Division-Coefficient Forms and the Artinian Eisenbud--Green--Harris Conjecture",
      "pdf_path": "preprints/Commuting-Division-Coefficient-Forms-and-the-Artinian-Eisenbud-Green-Harris-Conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Commuting-Division-Coefficient-Forms-and-the-Artinian-Eisenbud-Green-Harris-Conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "201:A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026",
      "family_id": "201",
      "discipline": "Algebra",
      "title": "A Counterexample to Kurosh\u2019s Division-Ring Problem",
      "pdf_path": "preprints/A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "202:The-Blockwise-Alperin-Weight-Conjecture-September-23-2026",
      "family_id": "202",
      "discipline": "Algebra",
      "title": "The Blockwise Alperin Weight Conjecture",
      "pdf_path": "preprints/The-Blockwise-Alperin-Weight-Conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Blockwise-Alperin-Weight-Conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "203:Donovans-Conjecture-over-Algebraic-Closures-of-Prime-Fields-September-24-2026",
      "family_id": "203",
      "discipline": "Algebra",
      "title": "Donovan's Conjecture over Algebraically Closed Fields",
      "pdf_path": "preprints/Donovans-Conjecture-over-Algebraic-Closures-of-Prime-Fields-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Donovans-Conjecture-over-Algebraic-Closures-of-Prime-Fields-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "203:Integral-Donovan-Finiteness-over-Witt-Vectors-September-25-2026",
      "family_id": "203",
      "discipline": "Algebra",
      "title": "Integral Donovan Finiteness over Witt Vectors",
      "pdf_path": "preprints/Integral-Donovan-Finiteness-over-Witt-Vectors-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Integral-Donovan-Finiteness-over-Witt-Vectors-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "204:Tensor-Saturation-for-Even-Spin-Groups-September-24-2026",
      "family_id": "204",
      "discipline": "Algebra",
      "title": "Tensor saturation for even spin groups",
      "pdf_path": "preprints/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "205:Universal-Tensor-Squares-for-Symmetric-Groups-September-24-2026",
      "family_id": "205",
      "discipline": "Algebra",
      "title": "Universal Tensor Squares for Symmetric Groups",
      "pdf_path": "preprints/Universal-Tensor-Squares-for-Symmetric-Groups-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Universal-Tensor-Squares-for-Symmetric-Groups-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/205.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "205:A-Cyclic-Polytabloid-Proof-of-Saxls-Conjecture-September-24-2026",
      "family_id": "205",
      "discipline": "Algebra",
      "title": "A Cyclic Polytabloid Proof of Saxl's Conjecture",
      "pdf_path": "preprints/A-Cyclic-Polytabloid-Proof-of-Saxls-Conjecture-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Cyclic-Polytabloid-Proof-of-Saxls-Conjecture-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/205.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "206:Finite-Congruence-Lattices-Characterization-and-Undecidability-September-24-2026",
      "family_id": "206",
      "discipline": "Algebra",
      "title": "Finite congruence lattices: characterization and undecidability",
      "pdf_path": "preprints/Finite-Congruence-Lattices-Characterization-and-Undecidability-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-Congruence-Lattices-Characterization-and-Undecidability-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/206.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "206:A-Negative-Solution-to-the-Finite-Lattice-Representation-Problem-September-24-2026",
      "family_id": "206",
      "discipline": "Algebra",
      "title": "A negative solution to the finite lattice representation problem",
      "pdf_path": "preprints/A-Negative-Solution-to-the-Finite-Lattice-Representation-Problem-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Negative-Solution-to-the-Finite-Lattice-Representation-Problem-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/206.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "207:The-l1-Bass-Conjecture-for-Discrete-Groups-October-5-2026",
      "family_id": "207",
      "discipline": "Algebra",
      "title": "The \u2113\u00b9-Bass Conjecture for Discrete Groups",
      "pdf_path": "preprints/The-l1-Bass-Conjecture-for-Discrete-Groups-October-5-2026/l1-bass-conjecture.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-l1-Bass-Conjecture-for-Discrete-Groups-October-5-2026/l1-bass-conjecture.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/207.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "207:The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026",
      "family_id": "207",
      "discipline": "Algebra",
      "title": "The Bass trace conjecture and the characteristic-zero Kaplansky idempotent conjecture",
      "pdf_path": "preprints/The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026/The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026/The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/207.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "208:Fiber-functors-for-finite-symmetric-tensor-categories-in-positive-characteristic-September-24-2026",
      "family_id": "208",
      "discipline": "Algebra",
      "title": "Fiber functors for finite symmetric tensor categories in positive characteristic",
      "pdf_path": "preprints/Fiber-functors-for-finite-symmetric-tensor-categories-in-positive-characteristic-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Fiber-functors-for-finite-symmetric-tensor-categories-in-positive-characteristic-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "209:An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026",
      "family_id": "209",
      "discipline": "Algebra",
      "title": "An integral counterexample to Gersten's conjecture",
      "pdf_path": "preprints/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "209:An-Integral-Degree-Three-Gersten-Counterexample-September-26-2026",
      "family_id": "209",
      "discipline": "Algebra",
      "title": "An integral degree-three Gersten counterexample",
      "pdf_path": "preprints/An-Integral-Degree-Three-Gersten-Counterexample-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-Integral-Degree-Three-Gersten-Counterexample-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "210:Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026",
      "family_id": "210",
      "discipline": "Algebra",
      "title": "Foulkes' conjecture for the sixth symmetric power",
      "pdf_path": "preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/210.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "210:Quadratic-Stabilization-of-the-Canonical-Foulkes-Howe-Map-September-25-2026",
      "family_id": "210",
      "discipline": "Algebra",
      "title": "Quadratic stabilization of the canonical Foulkes--Howe map",
      "pdf_path": "preprints/Quadratic-Stabilization-of-the-Canonical-Foulkes-Howe-Map-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Quadratic-Stabilization-of-the-Canonical-Foulkes-Howe-Map-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/210.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "211:Random-Walks-on-Critical-FK-Ising-Maps-and-Liouville-Brownian-Motion-October-5-2026",
      "family_id": "211",
      "discipline": "Probability and statistical mechanics",
      "title": "Random Walks on Critical FK\u2013Ising Maps and Liouville Brownian Motion",
      "pdf_path": "preprints/Random-Walks-on-Critical-FK-Ising-Maps-and-Liouville-Brownian-Motion-October-5-2026/fk-ising-walk-limit.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Random-Walks-on-Critical-FK-Ising-Maps-and-Liouville-Brownian-Motion-October-5-2026/fk-ising-walk-limit.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/211.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "211:Spectral-convergence-for-critical-FK-Ising-planar-maps-October-5-2026",
      "family_id": "211",
      "discipline": "Probability and statistical mechanics",
      "title": "Spectral convergence for critical FK\u2013Ising planar maps",
      "pdf_path": "preprints/Spectral-convergence-for-critical-FK-Ising-planar-maps-October-5-2026/spectral-convergence-critical-fk-ising-planar-maps.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Spectral-convergence-for-critical-FK-Ising-planar-maps-October-5-2026/spectral-convergence-critical-fk-ising-planar-maps.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/211.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "211:A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026",
      "family_id": "211",
      "discipline": "Probability and statistical mechanics",
      "title": "A Linear Clock for Random Walk on Tree-Weighted Planar Maps",
      "pdf_path": "preprints/A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026/linear-clock-random-walk-tree-weighted-planar-maps.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026/linear-clock-random-walk-tree-weighted-planar-maps.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/211.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "211:Canonical-conformal-limits-of-subcritical-FK-planar-maps-September-24-2026",
      "family_id": "211",
      "discipline": "Probability and statistical mechanics",
      "title": "Canonical conformal limits of subcritical FK planar maps",
      "pdf_path": "preprints/Canonical-conformal-limits-of-subcritical-FK-planar-maps-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Canonical-conformal-limits-of-subcritical-FK-planar-maps-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/211.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "211:The-critical-Liouville-quantum-sphere-and-geometric-limits-of-FK-maps-at-q-equals-4-September-24-2026",
      "family_id": "211",
      "discipline": "Probability and statistical mechanics",
      "title": "The critical Liouville quantum sphere and geometric limits of FK maps at q=4",
      "pdf_path": "preprints/The-critical-Liouville-quantum-sphere-and-geometric-limits-of-FK-maps-at-q-equals-4-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-critical-Liouville-quantum-sphere-and-geometric-limits-of-FK-maps-at-q-equals-4-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/211.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "211:Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026",
      "family_id": "211",
      "discipline": "Probability and statistical mechanics",
      "title": "Metric-measure limits of subcritical FK and spanning-tree planar maps",
      "pdf_path": "preprints/Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/211.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "211:Brownian-continuum-random-tree-limits-of-finite-Fortuin-Kasteleyn-maps-above-four-September-24-2026",
      "family_id": "211",
      "discipline": "Probability and statistical mechanics",
      "title": "Brownian continuum random tree limits of finite Fortuin\u2013Kasteleyn maps above four",
      "pdf_path": "preprints/Brownian-continuum-random-tree-limits-of-finite-Fortuin-Kasteleyn-maps-above-four-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Brownian-continuum-random-tree-limits-of-finite-Fortuin-Kasteleyn-maps-above-four-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/211.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "212:No-bigeodesics-in-planar-first-passage-percolation-September-24-2026",
      "family_id": "212",
      "discipline": "Probability and statistical mechanics",
      "title": "No bigeodesics in planar first-passage percolation",
      "pdf_path": "preprints/No-bigeodesics-in-planar-first-passage-percolation-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/No-bigeodesics-in-planar-first-passage-percolation-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/212.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "212:Strict-convexity-and-differentiability-of-the-planar-exponential-first-passage-limit-shape-September-24-2026",
      "family_id": "212",
      "discipline": "Probability and statistical mechanics",
      "title": "Strict convexity and differentiability of the planar exponential first-passage limit shape",
      "pdf_path": "preprints/Strict-convexity-and-differentiability-of-the-planar-exponential-first-passage-limit-shape-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Strict-convexity-and-differentiability-of-the-planar-exponential-first-passage-limit-shape-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/212.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "213:Critical-bond-and-site-percolation-on-the-cubic-lattice-September-24-2026",
      "family_id": "213",
      "discipline": "Probability and statistical mechanics",
      "title": "Critical bond and site percolation on the cubic lattice",
      "pdf_path": "preprints/Critical-bond-and-site-percolation-on-the-cubic-lattice-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Critical-bond-and-site-percolation-on-the-cubic-lattice-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/213.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "213:No-percolation-at-criticality-on-quasi-transitive-graphs-September-24-2026",
      "family_id": "213",
      "discipline": "Probability and statistical mechanics",
      "title": "No percolation at criticality on quasi-transitive graphs",
      "pdf_path": "preprints/No-percolation-at-criticality-on-quasi-transitive-graphs-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/No-percolation-at-criticality-on-quasi-transitive-graphs-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/213.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "214:Nonuniqueness-of-percolation-on-nonamenable-quasi-transitive-graphs-September-24-2026",
      "family_id": "214",
      "discipline": "Probability and statistical mechanics",
      "title": "Nonuniqueness of percolation on nonamenable quasi-transitive graphs",
      "pdf_path": "preprints/Nonuniqueness-of-percolation-on-nonamenable-quasi-transitive-graphs-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nonuniqueness-of-percolation-on-nonamenable-quasi-transitive-graphs-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/214.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "215:The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026",
      "family_id": "215",
      "discipline": "Probability and statistical mechanics",
      "title": "The canonical massive continuum limit of the two-dimensional O(3) model",
      "pdf_path": "preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/massive-continuum-o3.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/massive-continuum-o3.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/215.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "215:An-Isolated-Particle-Pole-for-the-Two-Dimensional-O3-Spin-Field-October-4-2026",
      "family_id": "215",
      "discipline": "Probability and statistical mechanics",
      "title": "An Isolated Particle Pole for the Two-Dimensional O(3) Spin Field",
      "pdf_path": "preprints/An-Isolated-Particle-Pole-for-the-Two-Dimensional-O3-Spin-Field-October-4-2026/o3-particle-pole.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-Isolated-Particle-Pole-for-the-Two-Dimensional-O3-Spin-Field-October-4-2026/o3-particle-pole.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/215.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "215:Exact-mass-asymptotics-for-the-two-dimensional-O4-lattice-model-October-5-2026",
      "family_id": "215",
      "discipline": "Probability and statistical mechanics",
      "title": "Exact mass asymptotics for the two-dimensional O(4) lattice model",
      "pdf_path": "preprints/Exact-mass-asymptotics-for-the-two-dimensional-O4-lattice-model-October-5-2026/exact-mass-o4.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-mass-asymptotics-for-the-two-dimensional-O4-lattice-model-October-5-2026/exact-mass-o4.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/215.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "215:Sharp-mass-bounds-for-the-two-dimensional-O4-model-September-23-2026",
      "family_id": "215",
      "discipline": "Probability and statistical mechanics",
      "title": "Sharp mass bounds for the two-dimensional O(4) model",
      "pdf_path": "preprints/Sharp-mass-bounds-for-the-two-dimensional-O4-model-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Sharp-mass-bounds-for-the-two-dimensional-O4-model-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/215.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "215:Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026",
      "family_id": "215",
      "discipline": "Probability and statistical mechanics",
      "title": "Exponential decay in two-dimensional classical O(n) models",
      "pdf_path": "preprints/Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/215.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "216:The-critical-logarithmic-correction-for-the-planar-XY-model-October-5-2026",
      "family_id": "216",
      "discipline": "Probability and statistical mechanics",
      "title": "The critical logarithmic correction for the planar XY model",
      "pdf_path": "preprints/The-critical-logarithmic-correction-for-the-planar-XY-model-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-critical-logarithmic-correction-for-the-planar-XY-model-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "216:Critical-Center-Magnetization-in-the-Planar-XY-Model-October-5-2026",
      "family_id": "216",
      "discipline": "Probability and statistical mechanics",
      "title": "Critical Center Magnetization in the Planar XY Model",
      "pdf_path": "preprints/Critical-Center-Magnetization-in-the-Planar-XY-Model-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Critical-Center-Magnetization-in-the-Planar-XY-Model-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "216:The-Critical-Spin-Field-of-the-Planar-XY-Model-October-5-2026",
      "family_id": "216",
      "discipline": "Probability and statistical mechanics",
      "title": "The Critical Spin Field of the Planar XY Model",
      "pdf_path": "preprints/The-Critical-Spin-Field-of-the-Planar-XY-Model-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Critical-Spin-Field-of-the-Planar-XY-Model-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "216:Essential-Singularity-of-the-Correlation-Length-in-the-Planar-XY-Model-October-5-2026",
      "family_id": "216",
      "discipline": "Probability and statistical mechanics",
      "title": "Essential Singularity of the Correlation Length in the Planar XY Model",
      "pdf_path": "preprints/Essential-Singularity-of-the-Correlation-Length-in-the-Planar-XY-Model-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Essential-Singularity-of-the-Correlation-Length-in-the-Planar-XY-Model-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "216:The-critical-correlation-exponent-of-the-planar-XY-model-September-24-2026",
      "family_id": "216",
      "discipline": "Probability and statistical mechanics",
      "title": "The critical correlation exponent of the planar XY model",
      "pdf_path": "preprints/The-critical-correlation-exponent-of-the-planar-XY-model-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-critical-correlation-exponent-of-the-planar-XY-model-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "216:BKT-universality-for-height-and-planar-spin-fields-September-24-2026",
      "family_id": "216",
      "discipline": "Probability and statistical mechanics",
      "title": "BKT universality for height and planar spin fields",
      "pdf_path": "preprints/BKT-universality-for-height-and-planar-spin-fields-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/BKT-universality-for-height-and-planar-spin-fields-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "217:The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026",
      "family_id": "217",
      "discipline": "Probability and statistical mechanics",
      "title": "The low-temperature Sherrington\u2013Kirkpatrick free-energy limiting law",
      "pdf_path": "preprints/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "217:The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026",
      "family_id": "217",
      "discipline": "Probability and statistical mechanics",
      "title": "The low-temperature Sherrington\u2013Kirkpatrick fluctuation scale",
      "pdf_path": "preprints/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "218:Quenched-SLE3-limits-for-general-weak-random-bond-Ising-models-October-5-2026",
      "family_id": "218",
      "discipline": "Probability and statistical mechanics",
      "title": "Quenched SLE\u2083 limits for general weak random-bond Ising models",
      "pdf_path": "preprints/Quenched-SLE3-limits-for-general-weak-random-bond-Ising-models-October-5-2026/general-weak-random-bond-ising.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Quenched-SLE3-limits-for-general-weak-random-bond-Ising-models-October-5-2026/general-weak-random-bond-ising.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/218.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "218:Quenched-SLE3-Universality-for-the-Weak-Random-Bond-Ising-Model-October-5-2026",
      "family_id": "218",
      "discipline": "Probability and statistical mechanics",
      "title": "Quenched SLE\u2083 Universality for the Weak Random-Bond Ising Model",
      "pdf_path": "preprints/Quenched-SLE3-Universality-for-the-Weak-Random-Bond-Ising-Model-October-5-2026/quenched-sle3-weak-random-bond-ising.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Quenched-SLE3-Universality-for-the-Weak-Random-Bond-Ising-Model-October-5-2026/quenched-sle3-weak-random-bond-ising.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/218.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "218:Logarithmic-Relative-Fluctuations-in-the-Weakly-Disordered-Planar-Ising-Model-October-5-2026",
      "family_id": "218",
      "discipline": "Probability and statistical mechanics",
      "title": "Logarithmic Relative Fluctuations in the Weakly Disordered Planar Ising Model",
      "pdf_path": "preprints/Logarithmic-Relative-Fluctuations-in-the-Weakly-Disordered-Planar-Ising-Model-October-5-2026/critical-relative-second-moment-weak-random-bond-ising.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Logarithmic-Relative-Fluctuations-in-the-Weakly-Disordered-Planar-Ising-Model-October-5-2026/critical-relative-second-moment-weak-random-bond-ising.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/218.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "218:Conformal-universality-of-bulk-Ising-correlations-under-weak-interactions-September-23-2026",
      "family_id": "218",
      "discipline": "Probability and statistical mechanics",
      "title": "Conformal universality of bulk Ising correlations under weak interactions",
      "pdf_path": "preprints/Conformal-universality-of-bulk-Ising-correlations-under-weak-interactions-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Conformal-universality-of-bulk-Ising-correlations-under-weak-interactions-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/218.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "218:SLE3-universality-for-weak-finite-range-Ising-interactions-September-23-2026",
      "family_id": "218",
      "discipline": "Probability and statistical mechanics",
      "title": "SLE3 universality for weak finite-range Ising interactions",
      "pdf_path": "preprints/SLE3-universality-for-weak-finite-range-Ising-interactions-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/SLE3-universality-for-weak-finite-range-Ising-interactions-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/218.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "218:Buffered-comparison-and-stopping-band-resolution-in-critical-Ising-September-23-2026",
      "family_id": "218",
      "discipline": "Probability and statistical mechanics",
      "title": "Buffered comparison and stopping-band resolution in critical Ising",
      "pdf_path": "preprints/Buffered-comparison-and-stopping-band-resolution-in-critical-Ising-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Buffered-comparison-and-stopping-band-resolution-in-critical-Ising-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/218.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "219:Fixed-energy-universality-for-weak-Anderson-disorder-on-random-regular-graphs-October-5-2026",
      "family_id": "219",
      "discipline": "Probability and statistical mechanics",
      "title": "Fixed-energy universality for weak Anderson disorder on random regular graphs",
      "pdf_path": "preprints/Fixed-energy-universality-for-weak-Anderson-disorder-on-random-regular-graphs-October-5-2026/fixed-energy-universality-weak-anderson-disorder-random-regular-graphs.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Fixed-energy-universality-for-weak-Anderson-disorder-on-random-regular-graphs-October-5-2026/fixed-energy-universality-weak-anderson-disorder-random-regular-graphs.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "219:GOE-bulk-universality-for-fixed-degree-random-regular-graphs-September-23-2026",
      "family_id": "219",
      "discipline": "Probability and statistical mechanics",
      "title": "GOE bulk universality for fixed-degree random regular graphs",
      "pdf_path": "preprints/GOE-bulk-universality-for-fixed-degree-random-regular-graphs-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/GOE-bulk-universality-for-fixed-degree-random-regular-graphs-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "220:A-directional-zero-one-law-for-finite-range-dependent-random-environments-October-5-2026",
      "family_id": "220",
      "discipline": "Probability and statistical mechanics",
      "title": "A directional zero\u2013one law for finite-range-dependent random environments",
      "pdf_path": "preprints/A-directional-zero-one-law-for-finite-range-dependent-random-environments-October-5-2026/directional-zero-one-finite-range.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-directional-zero-one-law-for-finite-range-dependent-random-environments-October-5-2026/directional-zero-one-finite-range.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/220.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "220:A-directional-zero-one-law-under-strict-ellipticity-September-23-2026",
      "family_id": "220",
      "discipline": "Probability and statistical mechanics",
      "title": "A directional zero\u2013one law under strict ellipticity",
      "pdf_path": "preprints/A-directional-zero-one-law-under-strict-ellipticity-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-directional-zero-one-law-under-strict-ellipticity-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/220.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "220:Directional-transience-implies-ballisticity-September-23-2026",
      "family_id": "220",
      "discipline": "Probability and statistical mechanics",
      "title": "Directional transience implies ballisticity",
      "pdf_path": "preprints/Directional-transience-implies-ballisticity-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Directional-transience-implies-ballisticity-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/220.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "221:The-Mezard-Parisi-formula-for-diluted-spin-glasses-September-23-2026",
      "family_id": "221",
      "discipline": "Probability and statistical mechanics",
      "title": "The M\u00e9zard\u2013Parisi formula for diluted spin glasses",
      "pdf_path": "preprints/The-Mezard-Parisi-formula-for-diluted-spin-glasses-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Mezard-Parisi-formula-for-diluted-spin-glasses-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/221.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "222:The-free-energy-of-the-Ising-random-perceptron-September-24-2026",
      "family_id": "222",
      "discipline": "Probability and statistical mechanics",
      "title": "The free energy of the Ising random perceptron",
      "pdf_path": "preprints/The-free-energy-of-the-Ising-random-perceptron-September-24-2026/The-free-energy-of-the-Ising-random-perceptron-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-free-energy-of-the-Ising-random-perceptron-September-24-2026/The-free-energy-of-the-Ising-random-perceptron-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/222.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "222:Microscopic-jamming-in-the-negative-spherical-perceptron-September-24-2026",
      "family_id": "222",
      "discipline": "Probability and statistical mechanics",
      "title": "Microscopic jamming in the negative spherical perceptron",
      "pdf_path": "preprints/Microscopic-jamming-in-the-negative-spherical-perceptron-September-24-2026/Microscopic-jamming-in-the-negative-spherical-perceptron-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Microscopic-jamming-in-the-negative-spherical-perceptron-September-24-2026/Microscopic-jamming-in-the-negative-spherical-perceptron-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/222.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "222:The-spherical-perceptron-with-bi-orthogonally-invariant-disorder-September-24-2026",
      "family_id": "222",
      "discipline": "Probability and statistical mechanics",
      "title": "The spherical perceptron with bi-orthogonally invariant disorder",
      "pdf_path": "preprints/The-spherical-perceptron-with-bi-orthogonally-invariant-disorder-September-24-2026/The-spherical-perceptron-with-bi-orthogonally-invariant-disorder-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-spherical-perceptron-with-bi-orthogonally-invariant-disorder-September-24-2026/The-spherical-perceptron-with-bi-orthogonally-invariant-disorder-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/222.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "222:The-free-energy-of-the-spherical-random-perceptron-September-24-2026",
      "family_id": "222",
      "discipline": "Probability and statistical mechanics",
      "title": "The free energy of the spherical random perceptron",
      "pdf_path": "preprints/The-free-energy-of-the-spherical-random-perceptron-September-24-2026/The-free-energy-of-the-spherical-random-perceptron-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-free-energy-of-the-spherical-random-perceptron-September-24-2026/The-free-energy-of-the-spherical-random-perceptron-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/222.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "223:Square-lattice-FK-interfaces-and-nested-loops-for-1-leq-q-lt-4-September-23-2026",
      "family_id": "223",
      "discipline": "Probability and statistical mechanics",
      "title": "Square-lattice FK interfaces and nested loops for 1 <= q < 4",
      "pdf_path": "preprints/Square-lattice-FK-interfaces-and-nested-loops-for-1-leq-q-lt-4-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Square-lattice-FK-interfaces-and-nested-loops-for-1-leq-q-lt-4-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "223:Self-dual-random-cluster-interfaces-below-one-September-23-2026",
      "family_id": "223",
      "discipline": "Probability and statistical mechanics",
      "title": "Self-dual random-cluster interfaces below one",
      "pdf_path": "preprints/Self-dual-random-cluster-interfaces-below-one-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Self-dual-random-cluster-interfaces-below-one-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "223:Quenched-SLE-Universality-for-Weakly-Disordered-FK-Ising-Interfaces-October-5-2026",
      "family_id": "223",
      "discipline": "Probability and statistical mechanics",
      "title": "Quenched SLE Universality for Weakly Disordered FK\u2013Ising Interfaces",
      "pdf_path": "preprints/Quenched-SLE-Universality-for-Weakly-Disordered-FK-Ising-Interfaces-October-5-2026/quenched-fk-ising.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Quenched-SLE-Universality-for-Weakly-Disordered-FK-Ising-Interfaces-October-5-2026/quenched-fk-ising.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "223:Thermal-FK-Ising-interfaces-and-massive-SLE-October-5-2026",
      "family_id": "223",
      "discipline": "Probability and statistical mechanics",
      "title": "Thermal FK\u2013Ising interfaces and massive SLE",
      "pdf_path": "preprints/Thermal-FK-Ising-interfaces-and-massive-SLE-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Thermal-FK-Ising-interfaces-and-massive-SLE-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "223:Natural-Occupation-Measures-for-Critical-Square-Lattice-FK-Interfaces-October-5-2026",
      "family_id": "223",
      "discipline": "Probability and statistical mechanics",
      "title": "Natural Occupation Measures for Critical Square-Lattice FK Interfaces",
      "pdf_path": "preprints/Natural-Occupation-Measures-for-Critical-Square-Lattice-FK-Interfaces-October-5-2026/natural-occupation-measures-critical-square-lattice-fk-interfaces.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Natural-Occupation-Measures-for-Critical-Square-Lattice-FK-Interfaces-October-5-2026/natural-occupation-measures-critical-square-lattice-fk-interfaces.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "223:Conformal-Limits-of-Critical-Square-Lattice-Random-Cluster-Interfaces-October-5-2026",
      "family_id": "223",
      "discipline": "Probability and statistical mechanics",
      "title": "Conformal Limits of Critical Square-Lattice Random-Cluster Interfaces",
      "pdf_path": "preprints/Conformal-Limits-of-Critical-Square-Lattice-Random-Cluster-Interfaces-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Conformal-Limits-of-Critical-Square-Lattice-Random-Cluster-Interfaces-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "224:From-critical-crossings-to-quenched-near-critical-universality-in-Voronoi-percolation-October-5-2026",
      "family_id": "224",
      "discipline": "Probability and statistical mechanics",
      "title": "From critical crossings to quenched near-critical universality in Voronoi percolation",
      "pdf_path": "preprints/From-critical-crossings-to-quenched-near-critical-universality-in-Voronoi-percolation-October-5-2026/critical-crossings-quenched-near-critical-universality-voronoi-percolation.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/From-critical-crossings-to-quenched-near-critical-universality-in-Voronoi-percolation-October-5-2026/critical-crossings-quenched-near-critical-universality-voronoi-percolation.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "224:A-Pivotal-Amplitude-for-Voronoi-Percolation-from-Cardys-Formula-October-5-2026",
      "family_id": "224",
      "discipline": "Probability and statistical mechanics",
      "title": "A Pivotal Amplitude for Voronoi Percolation from Cardy's Formula",
      "pdf_path": "preprints/A-Pivotal-Amplitude-for-Voronoi-Percolation-from-Cardys-Formula-October-5-2026/voronoi-pivotal-amplitude.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Pivotal-Amplitude-for-Voronoi-Percolation-from-Cardys-Formula-October-5-2026/voronoi-pivotal-amplitude.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "224:Cardys-formula-for-critical-Poisson-Voronoi-percolation-September-23-2026",
      "family_id": "224",
      "discipline": "Probability and statistical mechanics",
      "title": "Cardy\u2019s formula for critical Poisson\u2013Voronoi percolation",
      "pdf_path": "preprints/Cardys-formula-for-critical-Poisson-Voronoi-percolation-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Cardys-formula-for-critical-Poisson-Voronoi-percolation-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "225:The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026",
      "family_id": "225",
      "discipline": "Probability and statistical mechanics",
      "title": "The Gaussian free field limit of the balanced six-vertex model with variance multiplier 1/arcsin(c/2)",
      "pdf_path": "preprints/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "226:The-curve-scaling-limit-of-half-plane-double-dimers-September-23-2026",
      "family_id": "226",
      "discipline": "Probability and statistical mechanics",
      "title": "The curve scaling limit of half-plane double dimers",
      "pdf_path": "preprints/The-curve-scaling-limit-of-half-plane-double-dimers-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-curve-scaling-limit-of-half-plane-double-dimers-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "227:Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026",
      "family_id": "227",
      "discipline": "Probability and statistical mechanics",
      "title": "Universality of critical quench autocorrelations in the Sherrington\u2013Kirkpatrick model",
      "pdf_path": "preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/227.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "227:Functional-universality-of-critical-SK-autocorrelations-October-5-2026",
      "family_id": "227",
      "discipline": "Probability and statistical mechanics",
      "title": "Functional universality of critical SK autocorrelations",
      "pdf_path": "preprints/Functional-universality-of-critical-SK-autocorrelations-October-5-2026/critical-sk-autocorrelations.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Functional-universality-of-critical-SK-autocorrelations-October-5-2026/critical-sk-autocorrelations.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/227.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "227:A-spectral-gap-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026",
      "family_id": "227",
      "discipline": "Probability and statistical mechanics",
      "title": "A spectral gap throughout the high-temperature Sherrington\u2013Kirkpatrick phase",
      "pdf_path": "preprints/A-spectral-gap-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-spectral-gap-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/227.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "227:Cutoff-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026",
      "family_id": "227",
      "discipline": "Probability and statistical mechanics",
      "title": "Cutoff throughout the high-temperature Sherrington\u2013Kirkpatrick phase",
      "pdf_path": "preprints/Cutoff-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Cutoff-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/227.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "227:Critical-slowing-down-in-the-Sherrington-Kirkpatrick-model-September-24-2026",
      "family_id": "227",
      "discipline": "Probability and statistical mechanics",
      "title": "Critical slowing down in the Sherrington\u2013Kirkpatrick model",
      "pdf_path": "preprints/Critical-slowing-down-in-the-Sherrington-Kirkpatrick-model-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Critical-slowing-down-in-the-Sherrington-Kirkpatrick-model-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/227.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "227:Stretched-exponential-barriers-for-typical-SK-initial-states-September-24-2026",
      "family_id": "227",
      "discipline": "Probability and statistical mechanics",
      "title": "Stretched-exponential barriers for typical SK initial states",
      "pdf_path": "preprints/Stretched-exponential-barriers-for-typical-SK-initial-states-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Stretched-exponential-barriers-for-typical-SK-initial-states-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/227.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "227:A-typical-start-upper-bound-for-low-temperature-SK-Glauber-dynamics-September-24-2026",
      "family_id": "227",
      "discipline": "Probability and statistical mechanics",
      "title": "A typical-start upper bound for low-temperature SK Glauber dynamics",
      "pdf_path": "preprints/A-typical-start-upper-bound-for-low-temperature-SK-Glauber-dynamics-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-typical-start-upper-bound-for-low-temperature-SK-Glauber-dynamics-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/227.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "227:Critical-mixing-in-the-Sherrington-Kirkpatrick-model-September-25-2026",
      "family_id": "227",
      "discipline": "Probability and statistical mechanics",
      "title": "Critical mixing in the Sherrington\u2013Kirkpatrick model",
      "pdf_path": "preprints/Critical-mixing-in-the-Sherrington-Kirkpatrick-model-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Critical-mixing-in-the-Sherrington-Kirkpatrick-model-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/227.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "228:A-continuum-temperature-singularity-for-a-radial-pair-potential-September-24-2026",
      "family_id": "228",
      "discipline": "Probability and statistical mechanics",
      "title": "A continuum temperature singularity for a radial pair potential",
      "pdf_path": "preprints/A-continuum-temperature-singularity-for-a-radial-pair-potential-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-continuum-temperature-singularity-for-a-radial-pair-potential-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/228.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "228:A-radial-continuum-phase-transition-with-algebraic-decay-September-24-2026",
      "family_id": "228",
      "discipline": "Probability and statistical mechanics",
      "title": "A radial continuum phase transition with algebraic decay",
      "pdf_path": "preprints/A-radial-continuum-phase-transition-with-algebraic-decay-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-radial-continuum-phase-transition-with-algebraic-decay-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/228.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "229:The-Reconstruction-Threshold-for-the-Ferromagnetic-Four-State-Potts-Model-October-5-2026",
      "family_id": "229",
      "discipline": "Probability and statistical mechanics",
      "title": "The Reconstruction Threshold for the Ferromagnetic Four-State Potts Model",
      "pdf_path": "preprints/The-Reconstruction-Threshold-for-the-Ferromagnetic-Four-State-Potts-Model-October-5-2026/four-state-potts.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Reconstruction-Threshold-for-the-Ferromagnetic-Four-State-Potts-Model-October-5-2026/four-state-potts.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/229.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "229:A-Capacity-Criterion-for-Four-State-Potts-Reconstruction-on-Trees-October-5-2026",
      "family_id": "229",
      "discipline": "Probability and statistical mechanics",
      "title": "A Capacity Criterion for Four-State Potts Reconstruction on Trees",
      "pdf_path": "preprints/A-Capacity-Criterion-for-Four-State-Potts-Reconstruction-on-Trees-October-5-2026/four-state-capacity.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Capacity-Criterion-for-Four-State-Potts-Reconstruction-on-Trees-October-5-2026/four-state-capacity.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/229.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "229:The-exact-reconstruction-threshold-for-the-three-state-symmetric-channel-September-25-2026",
      "family_id": "229",
      "discipline": "Probability and statistical mechanics",
      "title": "The exact reconstruction threshold for the three-state symmetric channel",
      "pdf_path": "preprints/The-exact-reconstruction-threshold-for-the-three-state-symmetric-channel-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-exact-reconstruction-threshold-for-the-three-state-symmetric-channel-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/229.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "230:An-exact-Hausdorff-gauge-for-SLE-September-25-2026",
      "family_id": "230",
      "discipline": "Probability and statistical mechanics",
      "title": "An exact Hausdorff gauge for SLE",
      "pdf_path": "preprints/An-exact-Hausdorff-gauge-for-SLE-September-25-2026/An-exact-Hausdorff-gauge-for-SLE-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-exact-Hausdorff-gauge-for-SLE-September-25-2026/An-exact-Hausdorff-gauge-for-SLE-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/230.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "230:An-explicit-exact-Hausdorff-gauge-for-SLE-September-26-2026",
      "family_id": "230",
      "discipline": "Probability and statistical mechanics",
      "title": "An explicit exact Hausdorff gauge for SLE",
      "pdf_path": "preprints/An-explicit-exact-Hausdorff-gauge-for-SLE-September-26-2026/An-explicit-exact-Hausdorff-gauge-for-SLE-September-26-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-explicit-exact-Hausdorff-gauge-for-SLE-September-26-2026/An-explicit-exact-Hausdorff-gauge-for-SLE-September-26-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/230.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "231:The-free-uniform-spanning-forest-is-a-factor-of-IID-September-25-2026",
      "family_id": "231",
      "discipline": "Probability and statistical mechanics",
      "title": "The free uniform spanning forest is a factor of IID",
      "pdf_path": "preprints/The-free-uniform-spanning-forest-is-a-factor-of-IID-September-25-2026/The-free-uniform-spanning-forest-is-a-factor-of-IID-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-free-uniform-spanning-forest-is-a-factor-of-IID-September-25-2026/The-free-uniform-spanning-forest-is-a-factor-of-IID-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/231.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "232:Gaussian-free-field-limits-of-weighted-integer-Lipschitz-heights-October-6-2026",
      "family_id": "232",
      "discipline": "Probability and statistical mechanics",
      "title": "Gaussian free-field limits of weighted integer Lipschitz heights",
      "pdf_path": "preprints/Gaussian-free-field-limits-of-weighted-integer-Lipschitz-heights-October-6-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Gaussian-free-field-limits-of-weighted-integer-Lipschitz-heights-October-6-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "232:The-Gaussian-free-field-limit-of-integer-Lipschitz-heights-with-two-arc-boundary-data-October-6-2026",
      "family_id": "232",
      "discipline": "Probability and statistical mechanics",
      "title": "The Gaussian free field limit of integer Lipschitz heights with two-arc boundary data",
      "pdf_path": "preprints/The-Gaussian-free-field-limit-of-integer-Lipschitz-heights-with-two-arc-boundary-data-October-6-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Gaussian-free-field-limit-of-integer-Lipschitz-heights-with-two-arc-boundary-data-October-6-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "232:Uniform-real-Lipschitz-surfaces-on-the-triangular-lattice-October-6-2026",
      "family_id": "232",
      "discipline": "Probability and statistical mechanics",
      "title": "Uniform real Lipschitz surfaces on the triangular lattice",
      "pdf_path": "preprints/Uniform-real-Lipschitz-surfaces-on-the-triangular-lattice-October-6-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-real-Lipschitz-surfaces-on-the-triangular-lattice-October-6-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "233:The-joint-scaling-limit-of-critical-Ashkin-Teller-currents-October-6-2026",
      "family_id": "233",
      "discipline": "Probability and statistical mechanics",
      "title": "The joint scaling limit of critical Ashkin-Teller currents",
      "pdf_path": "preprints/The-joint-scaling-limit-of-critical-Ashkin-Teller-currents-October-6-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-joint-scaling-limit-of-critical-Ashkin-Teller-currents-October-6-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "234:All-temperature-pressure-for-orthogonally-invariant-Ising-spin-glasses-September-25-2026",
      "family_id": "234",
      "discipline": "Probability and statistical mechanics",
      "title": "All-temperature pressure for orthogonally invariant Ising spin glasses",
      "pdf_path": "preprints/All-temperature-pressure-for-orthogonally-invariant-Ising-spin-glasses-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/All-temperature-pressure-for-orthogonally-invariant-Ising-spin-glasses-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/234.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "235:A-Limiting-Satisfiability-Threshold-for-Every-Fixed-Clause-Size-September-25-2026",
      "family_id": "235",
      "discipline": "Probability and statistical mechanics",
      "title": "A Limiting Satisfiability Threshold for Every Fixed Clause Size",
      "pdf_path": "preprints/A-Limiting-Satisfiability-Threshold-for-Every-Fixed-Clause-Size-September-25-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Limiting-Satisfiability-Threshold-for-Every-Fixed-Clause-Size-September-25-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/235.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "235:Linear-Variance-of-the-Random-3-SAT-Hitting-Time-October-5-2026",
      "family_id": "235",
      "discipline": "Probability and statistical mechanics",
      "title": "Linear Variance of the Random 3-SAT Hitting Time",
      "pdf_path": "preprints/Linear-Variance-of-the-Random-3-SAT-Hitting-Time-October-5-2026/linear-variance-of-the-random-3-sat-hitting-time.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Linear-Variance-of-the-Random-3-SAT-Hitting-Time-October-5-2026/linear-variance-of-the-random-3-sat-hitting-time.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/235.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "235:Variance-of-the-Random-k-SAT-Hitting-Time-September-27-2026",
      "family_id": "235",
      "discipline": "Probability and statistical mechanics",
      "title": "Variance of the Random k-SAT Hitting Time",
      "pdf_path": "preprints/Variance-of-the-Random-k-SAT-Hitting-Time-September-27-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Variance-of-the-Random-k-SAT-Hitting-Time-September-27-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/235.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "235:Computing-the-Random-3-SAT-Threshold-September-27-2026",
      "family_id": "235",
      "discipline": "Probability and statistical mechanics",
      "title": "Computing the Random 3-SAT Threshold",
      "pdf_path": "preprints/Computing-the-Random-3-SAT-Threshold-September-27-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Computing-the-Random-3-SAT-Threshold-September-27-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/235.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "236:The-sharp-factor-of-IID-threshold-for-the-free-Ising-model-on-regular-trees-September-26-2026",
      "family_id": "236",
      "discipline": "Probability and statistical mechanics",
      "title": "The sharp factor-of-IID threshold for the free Ising model on regular trees",
      "pdf_path": "preprints/The-sharp-factor-of-IID-threshold-for-the-free-Ising-model-on-regular-trees-September-26-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-sharp-factor-of-IID-threshold-for-the-free-Ising-model-on-regular-trees-September-26-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/236.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "237:Radial-transfer-estimates-and-polygon-length-laws-for-honeycomb-walks-September-26-2026",
      "family_id": "237",
      "discipline": "Probability and statistical mechanics",
      "title": "Radial transfer estimates and polygon length laws for honeycomb walks",
      "pdf_path": "preprints/Radial-transfer-estimates-and-polygon-length-laws-for-honeycomb-walks-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Radial-transfer-estimates-and-polygon-length-laws-for-honeycomb-walks-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/237.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "237:Critical-honeycomb-chords-with-prescribed-boundary-endpoints-September-26-2026",
      "family_id": "237",
      "discipline": "Probability and statistical mechanics",
      "title": "Critical honeycomb chords with prescribed boundary endpoints",
      "pdf_path": "preprints/Critical-honeycomb-chords-with-prescribed-boundary-endpoints-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Critical-honeycomb-chords-with-prescribed-boundary-endpoints-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/237.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "237:Cylinder-loop-weights-and-planar-nesting-September-26-2026",
      "family_id": "237",
      "discipline": "Probability and statistical mechanics",
      "title": "Cylinder loop weights and planar nesting",
      "pdf_path": "preprints/Cylinder-loop-weights-and-planar-nesting-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Cylinder-loop-weights-and-planar-nesting-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/237.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "237:Mass-and-covering-exponents-for-fixed-length-honeycomb-walks-September-26-2026",
      "family_id": "237",
      "discipline": "Probability and statistical mechanics",
      "title": "Mass and covering exponents for fixed-length honeycomb walks",
      "pdf_path": "preprints/Mass-and-covering-exponents-for-fixed-length-honeycomb-walks-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Mass-and-covering-exponents-for-fixed-length-honeycomb-walks-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/237.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "237:Signed-cylinder-propagation-and-marked-polygons-on-the-honeycomb-lattice-September-26-2026",
      "family_id": "237",
      "discipline": "Probability and statistical mechanics",
      "title": "Signed cylinder propagation and marked polygons on the honeycomb lattice",
      "pdf_path": "preprints/Signed-cylinder-propagation-and-marked-polygons-on-the-honeycomb-lattice-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Signed-cylinder-propagation-and-marked-polygons-on-the-honeycomb-lattice-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/237.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "237:Cylinder-amplitudes-and-logarithmic-bridge-length-windows-on-the-honeycomb-lattice-September-26-2026",
      "family_id": "237",
      "discipline": "Probability and statistical mechanics",
      "title": "Cylinder amplitudes and logarithmic bridge-length windows on the honeycomb lattice",
      "pdf_path": "preprints/Cylinder-amplitudes-and-logarithmic-bridge-length-windows-on-the-honeycomb-lattice-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Cylinder-amplitudes-and-logarithmic-bridge-length-windows-on-the-honeycomb-lattice-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/237.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "237:Marked-polygon-correlations-and-one-arc-bounds-September-26-2026",
      "family_id": "237",
      "discipline": "Probability and statistical mechanics",
      "title": "Marked polygon correlations and one-arc bounds",
      "pdf_path": "preprints/Marked-polygon-correlations-and-one-arc-bounds-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Marked-polygon-correlations-and-one-arc-bounds-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/237.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "237:Disk-transfer-representations-and-confined-bridge-mass-September-26-2026",
      "family_id": "237",
      "discipline": "Probability and statistical mechanics",
      "title": "Disk transfer representations and confined bridge mass",
      "pdf_path": "preprints/Disk-transfer-representations-and-confined-bridge-mass-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Disk-transfer-representations-and-confined-bridge-mass-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/237.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "237:Polynomial-vacuum-representations-and-bridge-mass-for-honeycomb-walks-September-26-2026",
      "family_id": "237",
      "discipline": "Probability and statistical mechanics",
      "title": "Polynomial vacuum representations and bridge mass for honeycomb walks",
      "pdf_path": "preprints/Polynomial-vacuum-representations-and-bridge-mass-for-honeycomb-walks-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Polynomial-vacuum-representations-and-bridge-mass-for-honeycomb-walks-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/237.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "237:Renewal-and-changes-of-law-for-critical-honeycomb-walks-September-26-2026",
      "family_id": "237",
      "discipline": "Probability and statistical mechanics",
      "title": "Renewal and changes of law for critical honeycomb walks",
      "pdf_path": "preprints/Renewal-and-changes-of-law-for-critical-honeycomb-walks-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Renewal-and-changes-of-law-for-critical-honeycomb-walks-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/237.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "237:Critical-strip-crossing-mass-on-the-honeycomb-lattice-September-26-2026",
      "family_id": "237",
      "discipline": "Probability and statistical mechanics",
      "title": "Critical strip-crossing mass on the honeycomb lattice",
      "pdf_path": "preprints/Critical-strip-crossing-mass-on-the-honeycomb-lattice-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Critical-strip-crossing-mass-on-the-honeycomb-lattice-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/237.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "237:Uniform-marked-polygon-estimates-and-sharp-finite-bridge-moments-September-26-2026",
      "family_id": "237",
      "discipline": "Probability and statistical mechanics",
      "title": "Uniform marked-polygon estimates and sharp finite bridge moments",
      "pdf_path": "preprints/Uniform-marked-polygon-estimates-and-sharp-finite-bridge-moments-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-marked-polygon-estimates-and-sharp-finite-bridge-moments-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/237.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "237:Cap-selected-amplitudes-and-triangle-chords-for-honeycomb-walks-September-26-2026",
      "family_id": "237",
      "discipline": "Probability and statistical mechanics",
      "title": "Cap-selected amplitudes and triangle chords for honeycomb walks",
      "pdf_path": "preprints/Cap-selected-amplitudes-and-triangle-chords-for-honeycomb-walks-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Cap-selected-amplitudes-and-triangle-chords-for-honeycomb-walks-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/237.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "238:Optimal-order-mixing-of-the-Thorp-shuffle-September-26-2026",
      "family_id": "238",
      "discipline": "Probability and statistical mechanics",
      "title": "Optimal-order mixing of the Thorp shuffle",
      "pdf_path": "preprints/Optimal-order-mixing-of-the-Thorp-shuffle-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Optimal-order-mixing-of-the-Thorp-shuffle-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/238.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "238:Random-coordinate-frames-and-partial-permutation-laws-September-26-2026",
      "family_id": "238",
      "discipline": "Probability and statistical mechanics",
      "title": "Random coordinate frames and partial permutation laws",
      "pdf_path": "preprints/Random-coordinate-frames-and-partial-permutation-laws-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Random-coordinate-frames-and-partial-permutation-laws-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/238.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "238:From-partial-permutation-information-to-Fourier-bounds-September-26-2026",
      "family_id": "238",
      "discipline": "Probability and statistical mechanics",
      "title": "From partial permutation information to Fourier bounds",
      "pdf_path": "preprints/From-partial-permutation-information-to-Fourier-bounds-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/From-partial-permutation-information-to-Fourier-bounds-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/238.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "238:Conditional-information-under-deterministic-coordinate-sweeps-September-26-2026",
      "family_id": "238",
      "discipline": "Probability and statistical mechanics",
      "title": "Conditional information under deterministic coordinate sweeps",
      "pdf_path": "preprints/Conditional-information-under-deterministic-coordinate-sweeps-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Conditional-information-under-deterministic-coordinate-sweeps-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/238.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "238:Conditional-permutations-in-a-revealed-switching-environment-September-26-2026",
      "family_id": "238",
      "discipline": "Probability and statistical mechanics",
      "title": "Conditional permutations in a revealed switching environment",
      "pdf_path": "preprints/Conditional-permutations-in-a-revealed-switching-environment-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Conditional-permutations-in-a-revealed-switching-environment-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/238.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "238:Routing-densities-and-representation-contraction-for-Thorp-sweeps-September-26-2026",
      "family_id": "238",
      "discipline": "Probability and statistical mechanics",
      "title": "Routing densities and representation contraction for Thorp sweeps",
      "pdf_path": "preprints/Routing-densities-and-representation-contraction-for-Thorp-sweeps-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Routing-densities-and-representation-contraction-for-Thorp-sweeps-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/238.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "238:Row-column-symmetry-and-contraction-of-coordinate-sweeps-September-26-2026",
      "family_id": "238",
      "discipline": "Probability and statistical mechanics",
      "title": "Row\u2013column symmetry and contraction of coordinate sweeps",
      "pdf_path": "preprints/Row-column-symmetry-and-contraction-of-coordinate-sweeps-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Row-column-symmetry-and-contraction-of-coordinate-sweeps-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Row-column-symmetry-and-contraction-of-coordinate-sweeps-September-26-2026/build/sections/introduction.tex",
          "extent": "entire 207-line introduction",
          "note": "Full permutation versus one-card marginal; occupied/all-copy overlap and other moment routes; existential absolute sweep constants.",
          "sha256": "0962dee5a8a157c1ae058aa50e5c593ceea3b8736f69282ff28762dd9c322d3b"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/238.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "238:Random-subspace-tests-and-trace-smoothing-for-coordinate-sweeps-September-26-2026",
      "family_id": "238",
      "discipline": "Probability and statistical mechanics",
      "title": "Random-subspace tests and trace smoothing for coordinate sweeps",
      "pdf_path": "preprints/Random-subspace-tests-and-trace-smoothing-for-coordinate-sweeps-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Random-subspace-tests-and-trace-smoothing-for-coordinate-sweeps-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Random-subspace-tests-and-trace-smoothing-for-coordinate-sweeps-September-26-2026/build/main.tex",
          "extent": "entire driver/abstract",
          "note": "All-size (1/2)n^-5 full-permutation statement; driver not full proof.",
          "sha256": "191bba3fe028c24220ba8f400a7abccd33e683716d0cf0d9eef43a5a08653ca0"
        },
        {
          "path": "preprints/Random-subspace-tests-and-trace-smoothing-for-coordinate-sweeps-September-26-2026/build/sections/introduction.tex",
          "extent": "entire 68-line introduction",
          "note": "Regular-trace theorem, all-size scope and geometric/sparse proof overview.",
          "sha256": "dfd4625b6ddb9d46a553f1557b0594e48c70c078e9dd3ec528bfec2fb02713b2"
        },
        {
          "path": "preprints/Random-subspace-tests-and-trace-smoothing-for-coordinate-sweeps-September-26-2026/build/sections/proof.tex",
          "extent": "lines 548\u2013633",
          "note": "Representation-range conclusion, large threshold/base power, bounded exponent recurrence and forward TV deduction; earlier proof not fully reviewed.",
          "sha256": "84272ab701a783ca55b1cc80ad9ed43d46a26db130783e911e50b44495d218dc"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/238.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "238:Compatibility-entropy-and-the-spectrum-of-a-Thorp-sweep-September-26-2026",
      "family_id": "238",
      "discipline": "Probability and statistical mechanics",
      "title": "Compatibility entropy and the spectrum of a Thorp sweep",
      "pdf_path": "preprints/Compatibility-entropy-and-the-spectrum-of-a-Thorp-sweep-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Compatibility-entropy-and-the-spectrum-of-a-Thorp-sweep-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/238.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "238:Signed-tensor-densities-and-diagram-budgets-for-coordinate-sweeps-September-26-2026",
      "family_id": "238",
      "discipline": "Probability and statistical mechanics",
      "title": "Signed tensor densities and diagram budgets for the Thorp shuffle",
      "pdf_path": "preprints/Signed-tensor-densities-and-diagram-budgets-for-coordinate-sweeps-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Signed-tensor-densities-and-diagram-budgets-for-coordinate-sweeps-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Signed-tensor-densities-and-diagram-budgets-for-coordinate-sweeps-September-26-2026/build/sections/00-introduction.tex",
          "extent": "entire 211-line introduction",
          "note": "Prescribed signed occurrences, asymptotic fixed-sweep full-density convergence, marks/entropy and query-access sampler consequence; selected SpinAngle alone does not include every mixing claim.",
          "sha256": "6a731d82a4d313de14f6c397b93451f55312d92060b85afcc5d064c204920191"
        },
        {
          "path": "preprints/Signed-tensor-densities-and-diagram-budgets-for-coordinate-sweeps-September-26-2026/build/sections/01-preliminaries.tex",
          "extent": "entire preliminaries section",
          "note": "Physical law, bit/sweep convention, finite norm gap and support bound.",
          "sha256": "3cfe194c8b9cbaa76f98afa17ed614388ac63637ad78d08f9ba9ef4f1e306907"
        },
        {
          "path": "preprints/Signed-tensor-densities-and-diagram-budgets-for-coordinate-sweeps-September-26-2026/build/sections/03-spin.tex",
          "extent": "lines 320\u2013462",
          "note": "Selected induction ending, full-deck amplification and shared-bit local-access corollary.",
          "sha256": "cd4f9551738391dc6c025d8d5a6369957d177d25b75f88360c5e510caada74e6"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/238.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "238:Conditional-coordinate-sweeps-and-analytic-transfer-September-26-2026",
      "family_id": "238",
      "discipline": "Probability and statistical mechanics",
      "title": "Conditional coordinate sweeps and analytic transfer",
      "pdf_path": "preprints/Conditional-coordinate-sweeps-and-analytic-transfer-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Conditional-coordinate-sweeps-and-analytic-transfer-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/238.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "238:A-strict-four-row-permanent-inequality-and-permutation-moments-September-26-2026",
      "family_id": "238",
      "discipline": "Probability and statistical mechanics",
      "title": "A strict four-row permanent inequality and permutation moments",
      "pdf_path": "preprints/A-strict-four-row-permanent-inequality-and-permutation-moments-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-strict-four-row-permanent-inequality-and-permutation-moments-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/238.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "239:The-sharp-exponential-rate-of-singularity-for-symmetric-Bernoulli-matrices-October-3-2026",
      "family_id": "239",
      "discipline": "Probability and statistical mechanics",
      "title": "The sharp exponential rate of singularity for symmetric Bernoulli matrices",
      "pdf_path": "preprints/The-sharp-exponential-rate-of-singularity-for-symmetric-Bernoulli-matrices-October-3-2026/symmetric-bernoulli-singularity.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-sharp-exponential-rate-of-singularity-for-symmetric-Bernoulli-matrices-October-3-2026/symmetric-bernoulli-singularity.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "239:The-sharp-singularity-rate-for-biased-symmetric-sign-matrices-October-4-2026",
      "family_id": "239",
      "discipline": "Probability and statistical mechanics",
      "title": "The sharp singularity rate for biased symmetric sign matrices",
      "pdf_path": "preprints/The-sharp-singularity-rate-for-biased-symmetric-sign-matrices-October-4-2026/biased-symmetric-sign-singularity.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-sharp-singularity-rate-for-biased-symmetric-sign-matrices-October-4-2026/biased-symmetric-sign-singularity.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "240:A-CH-Obstruction-to-a-Prescribed-Categoricity-Threshold-September-24-2026",
      "family_id": "240",
      "discipline": "Mathematical logic",
      "title": "A CH obstruction to a prescribed categoricity threshold",
      "pdf_path": "preprints/A-CH-Obstruction-to-a-Prescribed-Categoricity-Threshold-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-CH-Obstruction-to-a-Prescribed-Categoricity-Threshold-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/240.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "240:Eventual-Categoricity-for-Abstract-Elementary-Classes-September-24-2026",
      "family_id": "240",
      "discipline": "Mathematical logic",
      "title": "Eventual categoricity for abstract elementary classes",
      "pdf_path": "preprints/Eventual-Categoricity-for-Abstract-Elementary-Classes-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Eventual-Categoricity-for-Abstract-Elementary-Classes-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/240.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "241:Rigidity-of-the-Turing-degrees-September-24-2026",
      "family_id": "241",
      "discipline": "Mathematical logic",
      "title": "Rigidity of the Turing degrees",
      "pdf_path": "preprints/Rigidity-of-the-Turing-degrees-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Rigidity-of-the-Turing-degrees-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/241.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "242:Single-fold-Diophantine-representations-September-24-2026",
      "family_id": "242",
      "discipline": "Mathematical logic",
      "title": "Single-fold Diophantine representations",
      "pdf_path": "preprints/Single-fold-Diophantine-representations-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Single-fold-Diophantine-representations-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/242.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "243:Choiceless-polynomial-time-with-counting-does-not-capture-polynomial-time-September-23-2026",
      "family_id": "243",
      "discipline": "Mathematical logic",
      "title": "Choiceless polynomial time with counting does not capture polynomial time",
      "pdf_path": "preprints/Choiceless-polynomial-time-with-counting-does-not-capture-polynomial-time-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Choiceless-polynomial-time-with-counting-does-not-capture-polynomial-time-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/243.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "243:Witnessed-symmetric-choice-is-strictly-stronger-than-choiceless-polynomial-time-with-counting-September-24-2026",
      "family_id": "243",
      "discipline": "Mathematical logic",
      "title": "Witnessed symmetric choice is strictly stronger than choiceless polynomial time with counting",
      "pdf_path": "preprints/Witnessed-symmetric-choice-is-strictly-stronger-than-choiceless-polynomial-time-with-counting-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Witnessed-symmetric-choice-is-strictly-stronger-than-choiceless-polynomial-time-with-counting-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/243.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "244:The-Partition-Principle-does-not-imply-Choice-September-24-2026",
      "family_id": "244",
      "discipline": "Mathematical logic",
      "title": "The Partition Principle does not imply Choice",
      "pdf_path": "preprints/The-Partition-Principle-does-not-imply-Choice-September-24-2026/partition-principle-without-choice.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Partition-Principle-does-not-imply-Choice-September-24-2026/partition-principle-without-choice.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/244.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "245:Weak-and-strong-normalization-in-pure-type-systems-September-25-2026",
      "family_id": "245",
      "discipline": "Mathematical logic",
      "title": "Weak and strong normalization in pure type systems",
      "pdf_path": "preprints/Weak-and-strong-normalization-in-pure-type-systems-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weak-and-strong-normalization-in-pure-type-systems-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Weak-and-strong-normalization-in-pure-type-systems-September-25-2026/build/sections/introduction.tex",
          "extent": "selected sections as documented in family addendum",
          "note": "The full introduction, syntax/typing definitions and main theorem were read, together with the selected formal scope. The claim applies to arbitrary pure type specifications, including nonfunctional relations, and to all legal expressions in all valid contexts under beta reduction inside annotations. One normalizing term or a successful finite evaluator test is insufficient. The theorem supplies no eta or added-rewrite-rule guarantee and no practical reduction-length bound. The proof and implementation correspondence have not been independently checked.",
          "sha256": "702b7d25ed32919dc78425670e6321d4fd2c322f82ea31a4c8078bc5c87fcfaa"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/245.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "246:A-Modulus-Proof-of-Cannons-Conjecture-September-23-2026",
      "family_id": "246",
      "discipline": "Group theory",
      "title": "A Modulus Proof of Cannon\u2019s Conjecture",
      "pdf_path": "preprints/A-Modulus-Proof-of-Cannons-Conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Modulus-Proof-of-Cannons-Conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/246.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "247:An-infinite-finitely-presented-residually-finite-2-group-October-5-2026",
      "family_id": "247",
      "discipline": "Group theory",
      "title": "An infinite finitely presented residually finite 2-group",
      "pdf_path": "preprints/An-infinite-finitely-presented-residually-finite-2-group-October-5-2026/residually-finite-torsion.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-infinite-finitely-presented-residually-finite-2-group-October-5-2026/residually-finite-torsion.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/247.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "247:An-infinite-finitely-presented-periodic-group-September-23-2026",
      "family_id": "247",
      "discipline": "Group theory",
      "title": "An infinite finitely presented periodic group",
      "pdf_path": "preprints/An-infinite-finitely-presented-periodic-group-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-infinite-finitely-presented-periodic-group-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/247.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "248:Thompsons-group-F-is-nonamenable-September-23-2026",
      "family_id": "248",
      "discipline": "Group theory",
      "title": "Thompson's group F is nonamenable",
      "pdf_path": "preprints/Thompsons-group-F-is-nonamenable-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Thompsons-group-F-is-nonamenable-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/248.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "249:A-finitely-generated-counterexample-to-the-Eilenberg-Ganea-conjecture-September-23-2026",
      "family_id": "249",
      "discipline": "Group theory",
      "title": "A finitely generated counterexample to the Eilenberg\u2013Ganea conjecture",
      "pdf_path": "preprints/A-finitely-generated-counterexample-to-the-Eilenberg-Ganea-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-finitely-generated-counterexample-to-the-Eilenberg-Ganea-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/249.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "250:Finite-algebraic-envelopes-and-the-Boone-Higman-conjecture-September-23-2026",
      "family_id": "250",
      "discipline": "Group theory",
      "title": "Finite algebraic envelopes and the Boone\u2013Higman conjecture",
      "pdf_path": "preprints/Finite-algebraic-envelopes-and-the-Boone-Higman-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-algebraic-envelopes-and-the-Boone-Higman-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/250.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "250:Simple-F-infinity-overgroups-of-groups-with-decidable-word-problem-September-23-2026",
      "family_id": "250",
      "discipline": "Group theory",
      "title": "Simple F\u221e overgroups of groups with decidable word problem",
      "pdf_path": "preprints/Simple-F-infinity-overgroups-of-groups-with-decidable-word-problem-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Simple-F-infinity-overgroups-of-groups-with-decidable-word-problem-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/250.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "250:A-universal-group-of-type-F-infinity-September-23-2026",
      "family_id": "250",
      "discipline": "Group theory",
      "title": "A universal group of type F\u221e",
      "pdf_path": "preprints/A-universal-group-of-type-F-infinity-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-universal-group-of-type-F-infinity-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/250.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "251:Unitarizability-Implies-Amenability-for-Countable-Groups-September-23-2026",
      "family_id": "251",
      "discipline": "Group theory",
      "title": "Unitarizability implies amenability for discrete groups",
      "pdf_path": "preprints/Unitarizability-Implies-Amenability-for-Countable-Groups-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unitarizability-Implies-Amenability-for-Countable-Groups-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/251.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "251:Strong-Ulam-Stability-Characterizes-Amenability-October-5-2026",
      "family_id": "251",
      "discipline": "Group theory",
      "title": "Strong Ulam Stability Characterizes Amenability",
      "pdf_path": "preprints/Strong-Ulam-Stability-Characterizes-Amenability-October-5-2026/strong-ulam-stability.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Strong-Ulam-Stability-Characterizes-Amenability-October-5-2026/strong-ulam-stability.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/251.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "252:a-torsion-free-hyperbolic-group-that-is-not-residually-finite-September-23-2026",
      "family_id": "252",
      "discipline": "Group theory",
      "title": "A torsion-free hyperbolic group that is not residually finite",
      "pdf_path": "preprints/a-torsion-free-hyperbolic-group-that-is-not-residually-finite-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/a-torsion-free-hyperbolic-group-that-is-not-residually-finite-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/252.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "253:An-Infinite-Finitely-Presented-Simple-Amenable-Group-September-23-2026",
      "family_id": "253",
      "discipline": "Group theory",
      "title": "An infinite finitely presented simple amenable group",
      "pdf_path": "preprints/An-Infinite-Finitely-Presented-Simple-Amenable-Group-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-Infinite-Finitely-Presented-Simple-Amenable-Group-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/253.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "254:Harmonic-heights-and-the-Artin-K-pi-1-conjecture-September-23-2026",
      "family_id": "254",
      "discipline": "Group theory",
      "title": "Harmonic heights and the Artin K(pi,1) conjecture",
      "pdf_path": "preprints/Harmonic-heights-and-the-Artin-K-pi-1-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Harmonic-heights-and-the-Artin-K-pi-1-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/254.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "254:An-Artin-group-with-no-geometric-CAT-0-action-September-23-2026",
      "family_id": "254",
      "discipline": "Group theory",
      "title": "An Artin group with no geometric CAT(0) action",
      "pdf_path": "preprints/An-Artin-group-with-no-geometric-CAT-0-action-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-Artin-group-with-no-geometric-CAT-0-action-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/254.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "254:Parabolic-intersections-in-Artin-groups-September-23-2026",
      "family_id": "254",
      "discipline": "Group theory",
      "title": "Parabolic intersections in Artin groups",
      "pdf_path": "preprints/Parabolic-intersections-in-Artin-groups-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Parabolic-intersections-in-Artin-groups-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Parabolic-intersections-in-Artin-groups-September-23-2026/build/sections/01_intro.tex",
          "extent": "selected sections as documented in family addendum",
          "note": "The parabolic-intersection introduction and effective-membership construction were read. Given a finite Coxeter matrix, subset, conjugator word and tested word, the source constructs an exact cyclotomic coefficient field, finite diagram algebras and a bounded projective complex, then cancels invertible entries to test membership. Taking the subset empty decides the word problem. The source explicitly asserts no complexity bound. Field degree, category dimensions, tensor-product complex growth and exact coefficients require measurement. The selected formal scope covers intersections, closures and structural consequences, not the membership algorithm. ArtinParabolicIntersections enables an external kernel in the inspected configuration. A membership decider alone is not an intersection constructor. The other two manuscripts in the family remain separately queued.",
          "sha256": "1e951033e449d034ca4221cf29ab580f8f2e6e188496f5c16ed0b79a082d6130"
        },
        {
          "path": "preprints/Parabolic-intersections-in-Artin-groups-September-23-2026/build/sections/08_stabilizers.tex",
          "extent": "selected sections as documented in family addendum",
          "note": "The parabolic-intersection introduction and effective-membership construction were read. Given a finite Coxeter matrix, subset, conjugator word and tested word, the source constructs an exact cyclotomic coefficient field, finite diagram algebras and a bounded projective complex, then cancels invertible entries to test membership. Taking the subset empty decides the word problem. The source explicitly asserts no complexity bound. Field degree, category dimensions, tensor-product complex growth and exact coefficients require measurement. The selected formal scope covers intersections, closures and structural consequences, not the membership algorithm. ArtinParabolicIntersections enables an external kernel in the inspected configuration. A membership decider alone is not an intersection constructor. The other two manuscripts in the family remain separately queued.",
          "sha256": "9cfceb9744fa8b4fea4d1cae255becb3ead856c486c8a6225f45a91fda2772b4"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/254.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "255:quasi-isometric-recognition-of-virtually-polycyclic-groups-September-24-2026",
      "family_id": "255",
      "discipline": "Group theory",
      "title": "Quasi-isometric recognition of virtually polycyclic groups",
      "pdf_path": "preprints/quasi-isometric-recognition-of-virtually-polycyclic-groups-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/quasi-isometric-recognition-of-virtually-polycyclic-groups-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/255.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "256:Nonsingular-systems-of-equations-over-arbitrary-groups-October-5-2026",
      "family_id": "256",
      "discipline": "Group theory",
      "title": "Nonsingular systems of equations over arbitrary groups",
      "pdf_path": "preprints/Nonsingular-systems-of-equations-over-arbitrary-groups-October-5-2026/nonsingular-systems-over-arbitrary-groups.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nonsingular-systems-of-equations-over-arbitrary-groups-October-5-2026/nonsingular-systems-over-arbitrary-groups.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/256.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "256:The-Kervaire-Theorem-for-Groups-September-24-2026",
      "family_id": "256",
      "discipline": "Group theory",
      "title": "The Kervaire theorem for groups",
      "pdf_path": "preprints/The-Kervaire-Theorem-for-Groups-September-24-2026/The-Kervaire-Theorem-for-Groups-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Kervaire-Theorem-for-Groups-September-24-2026/The-Kervaire-Theorem-for-Groups-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/256.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "257:A-hyperbolic-group-with-no-geometric-CAT0-action-September-25-2026",
      "family_id": "257",
      "discipline": "Group theory",
      "title": "A hyperbolic group with no geometric CAT(0) action",
      "pdf_path": "preprints/A-hyperbolic-group-with-no-geometric-CAT0-action-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-hyperbolic-group-with-no-geometric-CAT0-action-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/257.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "258:Baumslag-Solitar-free-one-relator-groups-are-hyperbolic-September-25-2026",
      "family_id": "258",
      "discipline": "Group theory",
      "title": "Baumslag-Solitar-free one-relator groups are hyperbolic",
      "pdf_path": "preprints/Baumslag-Solitar-free-one-relator-groups-are-hyperbolic-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Baumslag-Solitar-free-one-relator-groups-are-hyperbolic-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "258:Virtual-compact-specialness-of-hyperbolic-one-relator-groups-September-25-2026",
      "family_id": "258",
      "discipline": "Group theory",
      "title": "Virtual compact specialness of hyperbolic one-relator groups",
      "pdf_path": "preprints/Virtual-compact-specialness-of-hyperbolic-one-relator-groups-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Virtual-compact-specialness-of-hyperbolic-one-relator-groups-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "259:A-group-without-fixed-price-October-5-2026",
      "family_id": "259",
      "discipline": "Group theory",
      "title": "A group without fixed price",
      "pdf_path": "preprints/A-group-without-fixed-price-October-5-2026/unequal-costs-rank-100-amalgam.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-group-without-fixed-price-October-5-2026/unequal-costs-rank-100-amalgam.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "260:The-spacetime-Penrose-inequality-with-charge-and-original-data-rigidity-October-5-2026",
      "family_id": "260",
      "discipline": "Mathematical physics",
      "title": "The spacetime Penrose inequality with charge and original-data rigidity",
      "pdf_path": "preprints/The-spacetime-Penrose-inequality-with-charge-and-original-data-rigidity-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-spacetime-Penrose-inequality-with-charge-and-original-data-rigidity-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/260.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "260:A-Charged-Reduction-of-the-Spacetime-Penrose-Inequality-in-Spatial-Dimensions-at-Least-Four-October-5-2026",
      "family_id": "260",
      "discipline": "Mathematical physics",
      "title": "A Charged Reduction of the Spacetime Penrose Inequality in Spatial Dimensions at Least Four",
      "pdf_path": "preprints/A-Charged-Reduction-of-the-Spacetime-Penrose-Inequality-in-Spatial-Dimensions-at-Least-Four-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Charged-Reduction-of-the-Spacetime-Penrose-Inequality-in-Spatial-Dimensions-at-Least-Four-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/260.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "260:Spacetime-Penrose-inequalities-enclosing-area-charge-and-rigidity-October-5-2026",
      "family_id": "260",
      "discipline": "Mathematical physics",
      "title": "Spacetime Penrose inequalities: enclosing area, charge, and rigidity",
      "pdf_path": "preprints/Spacetime-Penrose-inequalities-enclosing-area-charge-and-rigidity-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Spacetime-Penrose-inequalities-enclosing-area-charge-and-rigidity-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/260.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "260:The-Kerr-Newman-Penrose-Inequality-for-Axisymmetric-Electrovacuum-Exteriors-October-5-2026",
      "family_id": "260",
      "discipline": "Mathematical physics",
      "title": "The Kerr\u2013Newman Penrose Inequality for Axisymmetric Electrovacuum Exteriors",
      "pdf_path": "preprints/The-Kerr-Newman-Penrose-Inequality-for-Axisymmetric-Electrovacuum-Exteriors-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Kerr-Newman-Penrose-Inequality-for-Axisymmetric-Electrovacuum-Exteriors-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/260.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "260:Electromagnetic-tails-and-the-Kerr-Newman-Penrose-inequality-October-5-2026",
      "family_id": "260",
      "discipline": "Mathematical physics",
      "title": "Electromagnetic tails and the Kerr\u2013Newman Penrose inequality",
      "pdf_path": "preprints/Electromagnetic-tails-and-the-Kerr-Newman-Penrose-inequality-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Electromagnetic-tails-and-the-Kerr-Newman-Penrose-inequality-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/260.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "260:The-nonmaximal-anti-de-Sitter-Penrose-Inequality-and-original-data-rigidity-October-5-2026",
      "family_id": "260",
      "discipline": "Mathematical physics",
      "title": "The nonmaximal anti-de Sitter Penrose Inequality and original-data rigidity",
      "pdf_path": "preprints/The-nonmaximal-anti-de-Sitter-Penrose-Inequality-and-original-data-rigidity-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-nonmaximal-anti-de-Sitter-Penrose-Inequality-and-original-data-rigidity-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/260.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "260:The-Penrose-inequality-for-maximal-asymptotically-hyperbolic-initial-data-October-5-2026",
      "family_id": "260",
      "discipline": "Mathematical physics",
      "title": "The Penrose inequality for maximal asymptotically hyperbolic initial data",
      "pdf_path": "preprints/The-Penrose-inequality-for-maximal-asymptotically-hyperbolic-initial-data-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Penrose-inequality-for-maximal-asymptotically-hyperbolic-initial-data-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/260.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "260:A-local-Penrose-inequality-for-conformal-perturbations-of-Schwarzschild-anti-de-Sitter-data-October-5-2026",
      "family_id": "260",
      "discipline": "Mathematical physics",
      "title": "A local Penrose inequality for conformal perturbations of Schwarzschild\u2013anti-de Sitter data",
      "pdf_path": "preprints/A-local-Penrose-inequality-for-conformal-perturbations-of-Schwarzschild-anti-de-Sitter-data-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-local-Penrose-inequality-for-conformal-perturbations-of-Schwarzschild-anti-de-Sitter-data-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/260.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "260:The-spacetime-Penrose-inequality-and-enclosing-area-September-27-2026",
      "family_id": "260",
      "discipline": "Mathematical physics",
      "title": "The spacetime Penrose inequality and enclosing area",
      "pdf_path": "preprints/The-spacetime-Penrose-inequality-and-enclosing-area-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-spacetime-Penrose-inequality-and-enclosing-area-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/260.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "260:Conformal-flow-and-the-Riemannian-Penrose-inequality-with-minimizing-frontiers-September-27-2026",
      "family_id": "260",
      "discipline": "Mathematical physics",
      "title": "Conformal flow and the Riemannian Penrose inequality with minimizing frontiers",
      "pdf_path": "preprints/Conformal-flow-and-the-Riemannian-Penrose-inequality-with-minimizing-frontiers-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Conformal-flow-and-the-Riemannian-Penrose-inequality-with-minimizing-frontiers-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/260.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "260:Equality-and-rigidity-in-the-spacetime-Penrose-inequality-September-27-2026",
      "family_id": "260",
      "discipline": "Mathematical physics",
      "title": "Equality and rigidity in the spacetime Penrose inequality",
      "pdf_path": "preprints/Equality-and-rigidity-in-the-spacetime-Penrose-inequality-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equality-and-rigidity-in-the-spacetime-Penrose-inequality-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/260.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "260:Boundary-graph-deformations-for-the-spacetime-Penrose-inequality-September-27-2026",
      "family_id": "260",
      "discipline": "Mathematical physics",
      "title": "Boundary graph deformations for the spacetime Penrose inequality",
      "pdf_path": "preprints/Boundary-graph-deformations-for-the-spacetime-Penrose-inequality-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Boundary-graph-deformations-for-the-spacetime-Penrose-inequality-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/260.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "260:Area-controlled-end-replacement-and-the-Bondi-Penrose-inequality-in-the-CKS-class-September-27-2026",
      "family_id": "260",
      "discipline": "Mathematical physics",
      "title": "Area-controlled end replacement and the Bondi Penrose inequality in the CKS class",
      "pdf_path": "preprints/Area-controlled-end-replacement-and-the-Bondi-Penrose-inequality-in-the-CKS-class-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Area-controlled-end-replacement-and-the-Bondi-Penrose-inequality-in-the-CKS-class-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/260.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "261:Absolutely-Continuous-Spectrum-for-Weak-Disorder-Anderson-Models-in-Dimensions-at-Least-Three-September-23-2026",
      "family_id": "261",
      "discipline": "Mathematical physics",
      "title": "Absolutely Continuous Spectrum for Weak-Disorder Anderson Models in Dimensions at Least Three",
      "pdf_path": "preprints/Absolutely-Continuous-Spectrum-for-Weak-Disorder-Anderson-Models-in-Dimensions-at-Least-Three-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Absolutely-Continuous-Spectrum-for-Weak-Disorder-Anderson-Models-in-Dimensions-at-Least-Three-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/261.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "261:Pure-Point-Spectrum-for-the-Two-Dimensional-Anderson-Model-at-Every-Positive-Disorder-September-23-2026",
      "family_id": "261",
      "discipline": "Mathematical physics",
      "title": "Pure-Point Spectrum for the Two-Dimensional Anderson Model at Every Positive Disorder",
      "pdf_path": "preprints/Pure-Point-Spectrum-for-the-Two-Dimensional-Anderson-Model-at-Every-Positive-Disorder-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Pure-Point-Spectrum-for-the-Two-Dimensional-Anderson-Model-at-Every-Positive-Disorder-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/261.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "262:Equality-cases-in-the-sharp-one-dimensional-matrix-Lieb-Thirring-inequality-October-5-2026",
      "family_id": "262",
      "discipline": "Mathematical physics",
      "title": "Equality cases in the sharp one-dimensional matrix Lieb\u2013Thirring inequality",
      "pdf_path": "preprints/Equality-cases-in-the-sharp-one-dimensional-matrix-Lieb-Thirring-inequality-October-5-2026/sharp-one-dimensional-lieb-thirring-inequalities-matrix-potentials.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equality-cases-in-the-sharp-one-dimensional-matrix-Lieb-Thirring-inequality-October-5-2026/sharp-one-dimensional-lieb-thirring-inequalities-matrix-potentials.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/262.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "262:Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials-October-5-2026",
      "family_id": "262",
      "discipline": "Mathematical physics",
      "title": "Sharp one-dimensional Lieb\u2013Thirring inequalities for matrix potentials",
      "pdf_path": "preprints/Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials-October-5-2026/sharp-matrix-lieb-thirring.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials-October-5-2026/sharp-matrix-lieb-thirring.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/262.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "262:Sharp-One-Dimensional-Lieb-Thirring-Constants-September-23-2026",
      "family_id": "262",
      "discipline": "Mathematical physics",
      "title": "Sharp one-dimensional Lieb\u2013Thirring constants",
      "pdf_path": "preprints/Sharp-One-Dimensional-Lieb-Thirring-Constants-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Sharp-One-Dimensional-Lieb-Thirring-Constants-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/262.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "263:Uniform-excess-charge-for-Coulomb-molecules-and-the-outer-radius-of-neutral-atoms-September-24-2026",
      "family_id": "263",
      "discipline": "Mathematical physics",
      "title": "Uniform excess charge for Coulomb molecules and the outer radius of neutral atoms",
      "pdf_path": "preprints/Uniform-excess-charge-for-Coulomb-molecules-and-the-outer-radius-of-neutral-atoms-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-excess-charge-for-Coulomb-molecules-and-the-outer-radius-of-neutral-atoms-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/263.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "263:Generalized-ionization-energies-for-full-Coulomb-atoms-September-24-2026",
      "family_id": "263",
      "discipline": "Mathematical physics",
      "title": "Generalized ionization energies for full Coulomb atoms",
      "pdf_path": "preprints/Generalized-ionization-energies-for-full-Coulomb-atoms-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Generalized-ionization-energies-for-full-Coulomb-atoms-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/263.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "263:Generalized-outer-electron-radii-of-neutral-Coulomb-atoms-September-24-2026",
      "family_id": "263",
      "discipline": "Mathematical physics",
      "title": "Generalized outer-electron radii of neutral Coulomb atoms",
      "pdf_path": "preprints/Generalized-outer-electron-radii-of-neutral-Coulomb-atoms-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Generalized-outer-electron-radii-of-neutral-Coulomb-atoms-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/263.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "264:Generic-Future-Inextendibility-with-Square-Integrable-Connection-Near-a-Fixed-Kerr-Spacetime-September-23-2026",
      "family_id": "264",
      "discipline": "Mathematical physics",
      "title": "Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime",
      "pdf_path": "preprints/Generic-Future-Inextendibility-with-Square-Integrable-Connection-Near-a-Fixed-Kerr-Spacetime-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Generic-Future-Inextendibility-with-Square-Integrable-Connection-Near-a-Fixed-Kerr-Spacetime-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "264:Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026",
      "family_id": "264",
      "discipline": "Mathematical physics",
      "title": "Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes",
      "pdf_path": "preprints/Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "264:Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026",
      "family_id": "264",
      "discipline": "Mathematical physics",
      "title": "Quantitative Near-Kerr Evolution and Generic C2 Future Inextendibility",
      "pdf_path": "preprints/Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "265:A-two-dimensional-area-law-from-a-global-spectral-gap-September-24-2026",
      "family_id": "265",
      "discipline": "Mathematical physics",
      "title": "A two-dimensional area law from a global spectral gap",
      "pdf_path": "preprints/A-two-dimensional-area-law-from-a-global-spectral-gap-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-two-dimensional-area-law-from-a-global-spectral-gap-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "265:Polynomial-PEPS-approximation-of-gapped-square-grid-ground-states-September-24-2026",
      "family_id": "265",
      "discipline": "Mathematical physics",
      "title": "Polynomial PEPS approximation of gapped square-grid ground states",
      "pdf_path": "preprints/Polynomial-PEPS-approximation-of-gapped-square-grid-ground-states-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Polynomial-PEPS-approximation-of-gapped-square-grid-ground-states-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "266:The-maximum-number-of-mutually-unbiased-bases-in-dimension-six-September-24-2026",
      "family_id": "266",
      "discipline": "Mathematical physics",
      "title": "The maximum number of mutually unbiased bases in dimension six",
      "pdf_path": "preprints/The-maximum-number-of-mutually-unbiased-bases-in-dimension-six-September-24-2026/The-maximum-number-of-mutually-unbiased-bases-in-dimension-six-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-maximum-number-of-mutually-unbiased-bases-in-dimension-six-September-24-2026/The-maximum-number-of-mutually-unbiased-bases-in-dimension-six-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/266.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "266:Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026",
      "family_id": "266",
      "discipline": "Mathematical physics",
      "title": "Exact Fourier certificates for complex Hadamard matrices of order six",
      "pdf_path": "preprints/Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026/Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026/Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/266.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "267:Bose-Einstein-condensation-at-positive-temperature-in-the-dilute-hard-sphere-gas-October-5-2026",
      "family_id": "267",
      "discipline": "Mathematical physics",
      "title": "Bose\u2013Einstein condensation at positive temperature in the dilute hard-sphere gas",
      "pdf_path": "preprints/Bose-Einstein-condensation-at-positive-temperature-in-the-dilute-hard-sphere-gas-October-5-2026/positive-temperature-hard-spheres.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Bose-Einstein-condensation-at-positive-temperature-in-the-dilute-hard-sphere-gas-October-5-2026/positive-temperature-hard-spheres.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/267.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "267:Quantum-Depletion-and-Momentum-Distribution-in-the-Dilute-Hard-Sphere-Bose-Gas-October-5-2026",
      "family_id": "267",
      "discipline": "Mathematical physics",
      "title": "Quantum Depletion and Momentum Distribution in the Dilute Hard-Sphere Bose Gas",
      "pdf_path": "preprints/Quantum-Depletion-and-Momentum-Distribution-in-the-Dilute-Hard-Sphere-Bose-Gas-October-5-2026/Quantum-Depletion-in-the-Dilute-Hard-Sphere-Bose-Gas.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Quantum-Depletion-and-Momentum-Distribution-in-the-Dilute-Hard-Sphere-Bose-Gas-October-5-2026/Quantum-Depletion-in-the-Dilute-Hard-Sphere-Bose-Gas.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/267.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "267:Quantum-Depletion-for-Fixed-Bounded-Repulsive-Potentials-October-5-2026",
      "family_id": "267",
      "discipline": "Mathematical physics",
      "title": "Quantum Depletion for Fixed Bounded Repulsive Potentials",
      "pdf_path": "preprints/Quantum-Depletion-for-Fixed-Bounded-Repulsive-Potentials-October-5-2026/fixed-repulsion-quantum-depletion.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Quantum-Depletion-for-Fixed-Bounded-Repulsive-Potentials-October-5-2026/fixed-repulsion-quantum-depletion.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/267.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "267:A-density-uniform-condensate-bound-for-dilute-Bose-gases-September-27-2026",
      "family_id": "267",
      "discipline": "Mathematical physics",
      "title": "A density-uniform condensate bound for dilute Bose gases",
      "pdf_path": "preprints/A-density-uniform-condensate-bound-for-dilute-Bose-gases-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-density-uniform-condensate-bound-for-dilute-Bose-gases-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/267.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "267:Ground-state-condensation-in-the-dilute-hard-sphere-gas-September-24-2026",
      "family_id": "267",
      "discipline": "Mathematical physics",
      "title": "Ground-state condensation in the dilute hard-sphere gas",
      "pdf_path": "preprints/Ground-state-condensation-in-the-dilute-hard-sphere-gas-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Ground-state-condensation-in-the-dilute-hard-sphere-gas-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/267.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "268:The-periodic-spin-one-Haldane-gap-September-24-2026",
      "family_id": "268",
      "discipline": "Mathematical physics",
      "title": "The periodic spin-one Haldane gap",
      "pdf_path": "preprints/The-periodic-spin-one-Haldane-gap-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-periodic-spin-one-Haldane-gap-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "268:A-boundary-field-gap-for-the-spin-one-Heisenberg-chain-September-24-2026",
      "family_id": "268",
      "discipline": "Mathematical physics",
      "title": "A boundary-field gap for the spin-one Heisenberg chain",
      "pdf_path": "preprints/A-boundary-field-gap-for-the-spin-one-Heisenberg-chain-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-boundary-field-gap-for-the-spin-one-Heisenberg-chain-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "269:Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026",
      "family_id": "269",
      "discipline": "Mathematical physics",
      "title": "Uniform Stability of the Spherical Laughlin Gap",
      "pdf_path": "preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/269.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "269:A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026",
      "family_id": "269",
      "discipline": "Mathematical physics",
      "title": "A Fock-space inequality and the Laughlin spectral gap",
      "pdf_path": "preprints/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/269.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "270:The-unique-threshold-bound-state-of-the-SU-N-BFSS-model-September-24-2026",
      "family_id": "270",
      "discipline": "Mathematical physics",
      "title": "The unique threshold bound state of the SU(N) BFSS model",
      "pdf_path": "preprints/The-unique-threshold-bound-state-of-the-SU-N-BFSS-model-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-unique-threshold-bound-state-of-the-SU-N-BFSS-model-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "270:Positive-eigenvalues-of-the-relative-SU-2-BFSS-Hamiltonian-October-5-2026",
      "family_id": "270",
      "discipline": "Mathematical physics",
      "title": "Positive eigenvalues of the relative SU(2) BFSS Hamiltonian",
      "pdf_path": "preprints/Positive-eigenvalues-of-the-relative-SU-2-BFSS-Hamiltonian-October-5-2026/positive-eigenvalues-relative-su2-bfss.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Positive-eigenvalues-of-the-relative-SU-2-BFSS-Hamiltonian-October-5-2026/positive-eigenvalues-relative-su2-bfss.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "271:Blochs-Law-for-Finite-Range-Heisenberg-Ferromagnets-in-Three-Dimensions-October-5-2026",
      "family_id": "271",
      "discipline": "Mathematical physics",
      "title": "Bloch's Law for Finite-Range Heisenberg Ferromagnets in Three Dimensions",
      "pdf_path": "preprints/Blochs-Law-for-Finite-Range-Heisenberg-Ferromagnets-in-Three-Dimensions-October-5-2026/bloch-law-heisenberg.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Blochs-Law-for-Finite-Range-Heisenberg-Ferromagnets-in-Three-Dimensions-October-5-2026/bloch-law-heisenberg.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/271.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "271:The-first-lattice-correction-to-Blochs-law-October-5-2026",
      "family_id": "271",
      "discipline": "Mathematical physics",
      "title": "The first lattice correction to Bloch's law",
      "pdf_path": "preprints/The-first-lattice-correction-to-Blochs-law-October-5-2026/first-lattice-correction-bloch-law.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-first-lattice-correction-to-Blochs-law-October-5-2026/first-lattice-correction-bloch-law.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/271.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "271:The-spherical-magnetization-law-for-the-three-dimensional-quantum-Heisenberg-ferromagnet-October-5-2026",
      "family_id": "271",
      "discipline": "Mathematical physics",
      "title": "The spherical magnetization law for the three-dimensional quantum Heisenberg ferromagnet",
      "pdf_path": "preprints/The-spherical-magnetization-law-for-the-three-dimensional-quantum-Heisenberg-ferromagnet-October-5-2026/spherical-magnetization.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-spherical-magnetization-law-for-the-three-dimensional-quantum-Heisenberg-ferromagnet-October-5-2026/spherical-magnetization.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/271.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "271:Spontaneous-magnetization-in-the-quantum-Heisenberg-ferromagnet-September-24-2026",
      "family_id": "271",
      "discipline": "Mathematical physics",
      "title": "Spontaneous magnetization in the quantum Heisenberg ferromagnet",
      "pdf_path": "preprints/Spontaneous-magnetization-in-the-quantum-Heisenberg-ferromagnet-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Spontaneous-magnetization-in-the-quantum-Heisenberg-ferromagnet-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/271.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "272:Entanglement-with-zero-distillable-secret-key-in-local-dimension-ten-September-27-2026",
      "family_id": "272",
      "discipline": "Mathematical physics",
      "title": "Entanglement with zero distillable secret key in local dimension ten",
      "pdf_path": "preprints/Entanglement-with-zero-distillable-secret-key-in-local-dimension-ten-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Entanglement-with-zero-distillable-secret-key-in-local-dimension-ten-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/272.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "273:The-entropy-photon-number-inequality-September-24-2026",
      "family_id": "273",
      "discipline": "Mathematical physics",
      "title": "The entropy photon-number inequality",
      "pdf_path": "preprints/The-entropy-photon-number-inequality-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-entropy-photon-number-inequality-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/273.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "274:Product-projection-localization-and-the-QAC0-parity-lower-bound-September-24-2026",
      "family_id": "274",
      "discipline": "Mathematical physics",
      "title": "Product-projection localization and the QAC0 parity lower bound",
      "pdf_path": "preprints/Product-projection-localization-and-the-QAC0-parity-lower-bound-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Product-projection-localization-and-the-QAC0-parity-lower-bound-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/274.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "274:Regular-trajectories-pruning-and-quantum-parity-September-24-2026",
      "family_id": "274",
      "discipline": "Mathematical physics",
      "title": "Regular trajectories, pruning and quantum parity",
      "pdf_path": "preprints/Regular-trajectories-pruning-and-quantum-parity-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Regular-trajectories-pruning-and-quantum-parity-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/274.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "275:Continuum-Coulomb-hardness-with-binary-nuclear-charges-September-24-2026",
      "family_id": "275",
      "discipline": "Mathematical physics",
      "title": "Continuum Coulomb hardness with binary nuclear charges",
      "pdf_path": "preprints/Continuum-Coulomb-hardness-with-binary-nuclear-charges-September-24-2026/Continuum-Coulomb-hardness-with-binary-nuclear-charges-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Continuum-Coulomb-hardness-with-binary-nuclear-charges-September-24-2026/Continuum-Coulomb-hardness-with-binary-nuclear-charges-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/275.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "275:QMA-hardness-of-continuum-Coulomb-energy-with-unit-nuclear-charges-September-24-2026",
      "family_id": "275",
      "discipline": "Mathematical physics",
      "title": "QMA-hardness of continuum Coulomb energy with unit nuclear charges",
      "pdf_path": "preprints/QMA-hardness-of-continuum-Coulomb-energy-with-unit-nuclear-charges-September-24-2026/QMA-hardness-of-continuum-Coulomb-energy-with-unit-nuclear-charges-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/QMA-hardness-of-continuum-Coulomb-energy-with-unit-nuclear-charges-September-24-2026/QMA-hardness-of-continuum-Coulomb-energy-with-unit-nuclear-charges-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/275.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "276:Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026",
      "family_id": "276",
      "discipline": "Mathematical physics",
      "title": "Classical capacity and entropy inequalities for generalized amplitude damping",
      "pdf_path": "preprints/Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/276.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "277:Threshold-parallel-repetition-for-finite-dimensional-entangled-games-September-25-2026",
      "family_id": "277",
      "discipline": "Mathematical physics",
      "title": "Threshold parallel repetition for finite-dimensional entangled games",
      "pdf_path": "preprints/Threshold-parallel-repetition-for-finite-dimensional-entangled-games-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Threshold-parallel-repetition-for-finite-dimensional-entangled-games-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/277.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "278:A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026",
      "family_id": "278",
      "discipline": "Mathematical physics",
      "title": "A Coulomb ground-state density without Kohn-Sham ensemble representation",
      "pdf_path": "preprints/A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "279:Exact-quantum-factoring-over-a-fixed-finite-gate-set-September-25-2026",
      "family_id": "279",
      "discipline": "Mathematical physics",
      "title": "Exact quantum factoring over a fixed finite gate set",
      "pdf_path": "preprints/Exact-quantum-factoring-over-a-fixed-finite-gate-set-September-25-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-quantum-factoring-over-a-fixed-finite-gate-set-September-25-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Exact-quantum-factoring-over-a-fixed-finite-gate-set-September-25-2026/build/sections/01-introduction.tex",
          "extent": "selected sections as documented in family addendum",
          "note": "The introduction and main theorem specify an ideal exact polynomial-time-uniform qubit circuit family over NOT, CNOT, Toffoli, Hadamard, diag(1,i), inverses and singly controlled versions. It outputs complete prime factorization with probability one in that ideal model. The introduction explicitly says its large polynomial parameters are not intended as practical resource improvements. This is neither a classical polynomial factoring method nor a noisy-hardware probability-one result. Replacing the gate set or claiming resource advantage requires separate translation and measurement. This strengthens the earlier application triage rather than replacing it.",
          "sha256": "6d001bb685b08498db9cf76aa31acb99c28928606025ca746ffa114eeb5be7cc"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/279.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "280:Strongly-rational-unitary-vertex-operator-algebras-and-conformal-nets-September-25-2026",
      "family_id": "280",
      "discipline": "Mathematical physics",
      "title": "Strongly rational unitary vertex operator algebras and conformal nets",
      "pdf_path": "preprints/Strongly-rational-unitary-vertex-operator-algebras-and-conformal-nets-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Strongly-rational-unitary-vertex-operator-algebras-and-conformal-nets-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/280.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "281:QAOA-attains-the-SK-ground-state-energy-in-the-thermodynamic-first-limit-September-25-2026",
      "family_id": "281",
      "discipline": "Mathematical physics",
      "title": "QAOA attains the SK ground-state energy in the thermodynamic-first limit",
      "pdf_path": "preprints/QAOA-attains-the-SK-ground-state-energy-in-the-thermodynamic-first-limit-September-25-2026/QAOA-attains-the-SK-ground-state-energy-in-the-thermodynamic-first-limit-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/QAOA-attains-the-SK-ground-state-energy-in-the-thermodynamic-first-limit-September-25-2026/QAOA-attains-the-SK-ground-state-energy-in-the-thermodynamic-first-limit-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/281.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "281:Full-support-of-the-zero-temperature-Sherrington-Kirkpatrick-order-parameter-September-27-2026",
      "family_id": "281",
      "discipline": "Mathematical physics",
      "title": "Full support of the zero-temperature Sherrington-Kirkpatrick order parameter",
      "pdf_path": "preprints/Full-support-of-the-zero-temperature-Sherrington-Kirkpatrick-order-parameter-September-27-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Full-support-of-the-zero-temperature-Sherrington-Kirkpatrick-order-parameter-September-27-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/281.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "282:Scale-and-conformal-symmetry-in-four-dimensional-operational-quantum-field-theory-September-26-2026",
      "family_id": "282",
      "discipline": "Mathematical physics",
      "title": "Scale and conformal symmetry in four-dimensional operational quantum field theory",
      "pdf_path": "preprints/Scale-and-conformal-symmetry-in-four-dimensional-operational-quantum-field-theory-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Scale-and-conformal-symmetry-in-four-dimensional-operational-quantum-field-theory-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "283:Polynomial-Time-Unitary-Synthesis-from-a-Boolean-Oracle-October-5-2026",
      "family_id": "283",
      "discipline": "Mathematical physics",
      "title": "Polynomial-Time Unitary Synthesis from a Boolean Oracle",
      "pdf_path": "preprints/Polynomial-Time-Unitary-Synthesis-from-a-Boolean-Oracle-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Polynomial-Time-Unitary-Synthesis-from-a-Boolean-Oracle-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "284:A-Nearly-Quartic-Separation-Between-Randomized-and-Quantum-Query-Complexity-October-5-2026",
      "family_id": "284",
      "discipline": "Mathematical physics",
      "title": "A Nearly Quartic Separation Between Randomized and Quantum Query Complexity",
      "pdf_path": "preprints/A-Nearly-Quartic-Separation-Between-Randomized-and-Quantum-Query-Complexity-October-5-2026/quartic-query-separation.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Nearly-Quartic-Separation-Between-Randomized-and-Quantum-Query-Complexity-October-5-2026/quartic-query-separation.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "285:A-Torsion-Free-Counterexample-to-Reduced-Baum-Connes-Injectivity-September-23-2026",
      "family_id": "285",
      "discipline": "Operator algebras",
      "title": "A torsion-free counterexample to reduced Baum\u2013Connes injectivity",
      "pdf_path": "preprints/A-Torsion-Free-Counterexample-to-Reduced-Baum-Connes-Injectivity-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Torsion-Free-Counterexample-to-Reduced-Baum-Connes-Injectivity-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "285:A-Torsion-Free-Counterexample-to-the-Kadison-Kaplansky-Projection-Conjecture-September-23-2026",
      "family_id": "285",
      "discipline": "Operator algebras",
      "title": "A torsion-free counterexample to the Kadison\u2013Kaplansky projection conjecture",
      "pdf_path": "preprints/A-Torsion-Free-Counterexample-to-the-Kadison-Kaplansky-Projection-Conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Torsion-Free-Counterexample-to-the-Kadison-Kaplansky-Projection-Conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "285:An-Irrational-Trace-Counterexample-to-Reduced-Baum-Connes-September-23-2026",
      "family_id": "285",
      "discipline": "Operator algebras",
      "title": "An irrational-trace counterexample to reduced Baum\u2013Connes",
      "pdf_path": "preprints/An-Irrational-Trace-Counterexample-to-Reduced-Baum-Connes-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-Irrational-Trace-Counterexample-to-Reduced-Baum-Connes-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "286:Arithmeticity-of-twisted-finite-correspondences-for-lattices-over-local-fields-September-23-2026",
      "family_id": "286",
      "discipline": "Operator algebras",
      "title": "Arithmeticity of twisted finite correspondences for lattices over local fields",
      "pdf_path": "preprints/Arithmeticity-of-twisted-finite-correspondences-for-lattices-over-local-fields-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Arithmeticity-of-twisted-finite-correspondences-for-lattices-over-local-fields-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "286:The-arithmetic-category-and-stable-recovery-of-lattice-factors-September-23-2026",
      "family_id": "286",
      "discipline": "Operator algebras",
      "title": "The arithmetic category and stable recovery of lattice factors",
      "pdf_path": "preprints/The-arithmetic-category-and-stable-recovery-of-lattice-factors-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-arithmetic-category-and-stable-recovery-of-lattice-factors-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "287:An-isomorphism-of-the-free-group-factors-September-23-2026",
      "family_id": "287",
      "discipline": "Operator algebras",
      "title": "An isomorphism of the free group factors",
      "pdf_path": "preprints/An-isomorphism-of-the-free-group-factors-September-23-2026/An-isomorphism-of-the-free-group-factors-September-23-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-isomorphism-of-the-free-group-factors-September-23-2026/An-isomorphism-of-the-free-group-factors-September-23-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/287.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "288:Kadisons-similarity-theorem-through-uniform-derivation-estimates-September-23-2026",
      "family_id": "288",
      "discipline": "Operator algebras",
      "title": "Kadison's similarity theorem through uniform derivation estimates",
      "pdf_path": "preprints/Kadisons-similarity-theorem-through-uniform-derivation-estimates-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Kadisons-similarity-theorem-through-uniform-derivation-estimates-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/288.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "289:Universal-strong-Kadison-Kastler-stability-September-23-2026",
      "family_id": "289",
      "discipline": "Operator algebras",
      "title": "Universal strong Kadison\u2013Kastler stability",
      "pdf_path": "preprints/Universal-strong-Kadison-Kastler-stability-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Universal-strong-Kadison-Kastler-stability-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/289.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "289:Near-Inclusions-of-von-Neumann-Algebras-Without-Small-Spatial-Embeddings-October-5-2026",
      "family_id": "289",
      "discipline": "Operator algebras",
      "title": "Near Inclusions of von Neumann Algebras Without Small Spatial Embeddings",
      "pdf_path": "preprints/Near-Inclusions-of-von-Neumann-Algebras-Without-Small-Spatial-Embeddings-October-5-2026/near-inclusions.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Near-Inclusions-of-von-Neumann-Algebras-Without-Small-Spatial-Embeddings-October-5-2026/near-inclusions.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/289.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "289:Close-Separable-Cstar-Algebras-Without-Spatial-Conjugacy-October-5-2026",
      "family_id": "289",
      "discipline": "Operator algebras",
      "title": "Close Separable C*-Algebras Without Spatial Conjugacy",
      "pdf_path": "preprints/Close-Separable-Cstar-Algebras-Without-Spatial-Conjugacy-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Close-Separable-Cstar-Algebras-Without-Spatial-Conjugacy-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/289.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "290:Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026",
      "family_id": "290",
      "discipline": "Operator algebras",
      "title": "Expected amenable subalgebras preserving core commutants",
      "pdf_path": "preprints/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/290.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "290:Bounded-recovery-for-modular-spectral-averages-September-23-2026",
      "family_id": "290",
      "discipline": "Operator algebras",
      "title": "Bounded recovery for modular spectral averages",
      "pdf_path": "preprints/Bounded-recovery-for-modular-spectral-averages-September-23-2026/Bounded-recovery-for-modular-spectral-averages-September-23-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Bounded-recovery-for-modular-spectral-averages-September-23-2026/Bounded-recovery-for-modular-spectral-averages-September-23-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/290.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "291:Equivariant-Jiang-Su-Stability-for-Amenable-Actions-in-the-Unital-Stably-Finite-Case-October-5-2026",
      "family_id": "291",
      "discipline": "Operator algebras",
      "title": "Equivariant Jiang\u2013Su Stability for Amenable Actions in the Unital Stably Finite Case",
      "pdf_path": "preprints/Equivariant-Jiang-Su-Stability-for-Amenable-Actions-in-the-Unital-Stably-Finite-Case-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equivariant-Jiang-Su-Stability-for-Amenable-Actions-in-the-Unital-Stably-Finite-Case-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/291.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "291:Cuntz-comparison-and-Jiang-Su-absorption-September-23-2026",
      "family_id": "291",
      "discipline": "Operator algebras",
      "title": "Cuntz comparison and Jiang\u2013Su absorption",
      "pdf_path": "preprints/Cuntz-comparison-and-Jiang-Su-absorption-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Cuntz-comparison-and-Jiang-Su-absorption-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/291.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "291:Nuclear-dimension-and-Jiang-Su-stability-without-elementary-subquotients-September-23-2026",
      "family_id": "291",
      "discipline": "Operator algebras",
      "title": "Nuclear dimension and Jiang\u2013Su stability without elementary subquotients",
      "pdf_path": "preprints/Nuclear-dimension-and-Jiang-Su-stability-without-elementary-subquotients-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nuclear-dimension-and-Jiang-Su-stability-without-elementary-subquotients-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/291.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "291:Tracial-projection-methods-and-uniform-property-Gamma-September-23-2026",
      "family_id": "291",
      "discipline": "Operator algebras",
      "title": "Tracial projection methods and uniform property Gamma",
      "pdf_path": "preprints/Tracial-projection-methods-and-uniform-property-Gamma-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Tracial-projection-methods-and-uniform-property-Gamma-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/291.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "292:An-explicit-obstruction-to-nuclear-norm-ultrapower-embeddings-September-23-2026",
      "family_id": "292",
      "discipline": "Operator algebras",
      "title": "An explicit obstruction to nuclear norm-ultrapower embeddings",
      "pdf_path": "preprints/An-explicit-obstruction-to-nuclear-norm-ultrapower-embeddings-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-explicit-obstruction-to-nuclear-norm-ultrapower-embeddings-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/292.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "293:Invariant-projection-counterexamples-for-every-irrational-rotation-September-27-2026",
      "family_id": "293",
      "discipline": "Operator algebras",
      "title": "Invariant-projection counterexamples for every irrational rotation",
      "pdf_path": "preprints/Invariant-projection-counterexamples-for-every-irrational-rotation-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Invariant-projection-counterexamples-for-every-irrational-rotation-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/293.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "293:Backward-intertwiners-and-a-transitive-commutant-September-27-2026",
      "family_id": "293",
      "discipline": "Operator algebras",
      "title": "Backward intertwiners and a transitive commutant",
      "pdf_path": "preprints/Backward-intertwiners-and-a-transitive-commutant-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Backward-intertwiners-and-a-transitive-commutant-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/293.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "294:A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026",
      "family_id": "294",
      "discipline": "Operator algebras",
      "title": "A counterexample to Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness",
      "pdf_path": "preprints/A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/294.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "295:Vanishing-of-higher-bounded-Hochschild-cohomology-September-23-2026",
      "family_id": "295",
      "discipline": "Operator algebras",
      "title": "Vanishing of higher bounded Hochschild cohomology",
      "pdf_path": "preprints/Vanishing-of-higher-bounded-Hochschild-cohomology-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Vanishing-of-higher-bounded-Hochschild-cohomology-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/295.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "296:Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026",
      "family_id": "296",
      "discipline": "Operator algebras",
      "title": "Relative generation and the generator problem for finite factors",
      "pdf_path": "preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/296.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "297:A-counterexample-to-Naimarks-problem-in-ZFC-September-24-2026",
      "family_id": "297",
      "discipline": "Operator algebras",
      "title": "A counterexample to Naimark's problem in ZFC",
      "pdf_path": "preprints/A-counterexample-to-Naimarks-problem-in-ZFC-September-24-2026/naimark-counterexample-zfc.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-counterexample-to-Naimarks-problem-in-ZFC-September-24-2026/naimark-counterexample-zfc.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/A-counterexample-to-Naimarks-problem-in-ZFC-September-24-2026/build/sections/introduction.tex",
          "extent": "entire 136-line introduction",
          "note": "Nonseparable simple unital counterexample with faithful trace, transfinite construction and prior-work context as source claims; no effective finite construction or independent historical verification.",
          "sha256": "1d6dd0bc157a40b3a57c4dbc57f1ecfb146cd5c691e41a484df26dbe580e3cf6"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/297.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "298:A-finite-entropy-separation-of-microstates-and-nonmicrostates-free-entropy-September-25-2026",
      "family_id": "298",
      "discipline": "Operator algebras",
      "title": "A finite-entropy separation of microstates and nonmicrostates free entropy",
      "pdf_path": "preprints/A-finite-entropy-separation-of-microstates-and-nonmicrostates-free-entropy-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-finite-entropy-separation-of-microstates-and-nonmicrostates-free-entropy-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/298.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "299:The-Kirchberg-Rordam-character-criterion-September-25-2026",
      "family_id": "299",
      "discipline": "Operator algebras",
      "title": "The Kirchberg\u2013R\u00f8rdam character criterion",
      "pdf_path": "preprints/The-Kirchberg-Rordam-character-criterion-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Kirchberg-Rordam-character-criterion-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/299.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "300:Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026",
      "family_id": "300",
      "discipline": "Operator algebras",
      "title": "Approximation Paving over Arbitrary Maximal Abelian Subalgebras",
      "pdf_path": "preprints/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "300:Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026",
      "family_id": "300",
      "discipline": "Operator algebras",
      "title": "Quadratic Strong-Operator Paving over Arbitrary Maximal Abelian Subalgebras",
      "pdf_path": "preprints/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "301:The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026",
      "family_id": "301",
      "discipline": "Operator algebras",
      "title": "The trace cone classifies Razak\u2013Jacelon stabilizations",
      "pdf_path": "preprints/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/301.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "302:Filtered-products-and-boundary-preserving-compression-in-complex-cobordism-September-25-2026",
      "family_id": "302",
      "discipline": "Operator algebras",
      "title": "Filtered products and boundary-preserving compression in complex cobordism",
      "pdf_path": "preprints/Filtered-products-and-boundary-preserving-compression-in-complex-cobordism-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Filtered-products-and-boundary-preserving-compression-in-complex-cobordism-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "302:Radius-of-comparison-equals-half-the-mean-dimension-September-25-2026",
      "family_id": "302",
      "discipline": "Operator algebras",
      "title": "Radius of comparison equals half the mean dimension",
      "pdf_path": "preprints/Radius-of-comparison-equals-half-the-mean-dimension-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Radius-of-comparison-equals-half-the-mean-dimension-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "303:Weak-pure-infiniteness-and-O-infinity-absorption-September-25-2026",
      "family_id": "303",
      "discipline": "Operator algebras",
      "title": "Weak pure infiniteness and O-infinity absorption",
      "pdf_path": "preprints/Weak-pure-infiniteness-and-O-infinity-absorption-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weak-pure-infiniteness-and-O-infinity-absorption-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/303.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "304:The-Hilbert-Smith-conjecture-in-every-finite-dimension-September-23-2026",
      "family_id": "304",
      "discipline": "Topology",
      "title": "The Hilbert\u2013Smith conjecture in every finite dimension",
      "pdf_path": "preprints/The-Hilbert-Smith-conjecture-in-every-finite-dimension-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Hilbert-Smith-conjecture-in-every-finite-dimension-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "305:A-boundary-only-obstruction-to-four-dimensional-disk-embedding-September-24-2026",
      "family_id": "305",
      "discipline": "Topology",
      "title": "A boundary-only obstruction to four-dimensional disk embedding",
      "pdf_path": "preprints/A-boundary-only-obstruction-to-four-dimensional-disk-embedding-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-boundary-only-obstruction-to-four-dimensional-disk-embedding-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "305:A-marked-tensor-obstruction-to-four-dimensional-disk-embedding-September-24-2026",
      "family_id": "305",
      "discipline": "Topology",
      "title": "A marked tensor obstruction to four-dimensional disk embedding",
      "pdf_path": "preprints/A-marked-tensor-obstruction-to-four-dimensional-disk-embedding-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-marked-tensor-obstruction-to-four-dimensional-disk-embedding-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "305:A-PD4-group-without-an-aspherical-manifold-model-September-24-2026",
      "family_id": "305",
      "discipline": "Topology",
      "title": "A PD4 group without an aspherical manifold model",
      "pdf_path": "preprints/A-PD4-group-without-an-aspherical-manifold-model-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-PD4-group-without-an-aspherical-manifold-model-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "306:Purely-Cosmetic-Surgery-on-Knots-in-the-Three-Sphere-September-23-2026",
      "family_id": "306",
      "discipline": "Topology",
      "title": "Purely cosmetic surgery on knots in the three-sphere",
      "pdf_path": "preprints/Purely-Cosmetic-Surgery-on-Knots-in-the-Three-Sphere-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Purely-Cosmetic-Surgery-on-Knots-in-the-Three-Sphere-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "307:Failure-of-rational-injectivity-for-maximal-coarse-assembly-October-5-2026",
      "family_id": "307",
      "discipline": "Topology",
      "title": "Failure of rational injectivity for maximal coarse assembly",
      "pdf_path": "preprints/Failure-of-rational-injectivity-for-maximal-coarse-assembly-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Failure-of-rational-injectivity-for-maximal-coarse-assembly-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/307.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "307:A-counterexample-to-the-coarse-Novikov-conjecture-September-23-2026",
      "family_id": "307",
      "discipline": "Topology",
      "title": "A counterexample to the coarse Novikov conjecture",
      "pdf_path": "preprints/A-counterexample-to-the-coarse-Novikov-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-counterexample-to-the-coarse-Novikov-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/307.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "308:Finite-Smith-Toda-Complexes-at-Varying-Primes-September-23-2026",
      "family_id": "308",
      "discipline": "Topology",
      "title": "Finite Smith\u2013Toda Complexes at Varying Primes",
      "pdf_path": "preprints/Finite-Smith-Toda-Complexes-at-Varying-Primes-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-Smith-Toda-Complexes-at-Varying-Primes-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "308:A-finite-Smith-Toda-complex-V4-at-the-prime-1009-September-23-2026",
      "family_id": "308",
      "discipline": "Topology",
      "title": "A finite Smith\u2013Toda complex V(4) at the prime 1009",
      "pdf_path": "preprints/A-finite-Smith-Toda-complex-V4-at-the-prime-1009-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-finite-Smith-Toda-complex-V4-at-the-prime-1009-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "309:The-Kervaire-Invariant-Problem-at-the-Prime-Three-September-24-2026",
      "family_id": "309",
      "discipline": "Topology",
      "title": "The Kervaire invariant problem at the prime three",
      "pdf_path": "preprints/The-Kervaire-Invariant-Problem-at-the-Prime-Three-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Kervaire-Invariant-Problem-at-the-Prime-Three-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "310:Rational-homology-and-Quillens-conjecture-September-24-2026",
      "family_id": "310",
      "discipline": "Topology",
      "title": "Rational homology and Quillen's conjecture",
      "pdf_path": "preprints/Rational-homology-and-Quillens-conjecture-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Rational-homology-and-Quillens-conjecture-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "311:Stabilizer-Orbits-and-Thick-Tensor-Ideals-of-Dualizable-Kn-Local-Spectra-September-24-2026",
      "family_id": "311",
      "discipline": "Topology",
      "title": "Stabilizer orbits and thick tensor ideals of dualizable K(n)-local spectra",
      "pdf_path": "preprints/Stabilizer-Orbits-and-Thick-Tensor-Ideals-of-Dualizable-Kn-Local-Spectra-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Stabilizer-Orbits-and-Thick-Tensor-Ideals-of-Dualizable-Kn-Local-Spectra-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "312:The-Grothendieck-homotopy-hypothesis-via-elementary-expansions-September-24-2026",
      "family_id": "312",
      "discipline": "Topology",
      "title": "The Grothendieck homotopy hypothesis via elementary expansions",
      "pdf_path": "preprints/The-Grothendieck-homotopy-hypothesis-via-elementary-expansions-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Grothendieck-homotopy-hypothesis-via-elementary-expansions-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/312.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "313:Finite-generation-for-the-Kn-local-sphere-September-24-2026",
      "family_id": "313",
      "discipline": "Topology",
      "title": "Finite generation for the K(n)-local sphere",
      "pdf_path": "preprints/Finite-generation-for-the-Kn-local-sphere-September-24-2026/Finite-generation-for-the-Kn-local-sphere-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-generation-for-the-Kn-local-sphere-September-24-2026/Finite-generation-for-the-Kn-local-sphere-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "314:Cyclic-Length-and-Chromatic-Fixed-Point-Loss-September-24-2026",
      "family_id": "314",
      "discipline": "Topology",
      "title": "Cyclic length and chromatic fixed-point loss",
      "pdf_path": "preprints/Cyclic-Length-and-Chromatic-Fixed-Point-Loss-September-24-2026/Cyclic-Length-and-Chromatic-Fixed-Point-Loss-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Cyclic-Length-and-Chromatic-Fixed-Point-Loss-September-24-2026/Cyclic-Length-and-Chromatic-Fixed-Point-Loss-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Cyclic-Length-and-Chromatic-Fixed-Point-Loss-September-24-2026/build/sections/01-introduction.tex",
          "extent": "selected sections as documented in family addendum",
          "note": "The introduction defines cyclic length as the shortest subnormal subgroup chain with cyclic successive quotients and claims equality with chromatic fixed-point loss for every finite p-group, embedded subgroup and nonnegative height. A cyclic quotient of order p squared counts once. The source gives two differently embedded subgroups in C_(p squared) times C_p with losses two and one. Abstract subgroup isomorphism type is insufficient. Exhaustive subgroup enumeration is a finite reference method, not a polynomial algorithm. The spectrum hypotheses and proof remain outside a subgroup calculator. No family formal-scope document is available.",
          "sha256": "8894c87e5a4f5ff766f3335a026104a3ecf6f8504d9c7fc0626a6188ceb6da82"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "315:The-Singer-conjecture-in-dimension-four-September-25-2026",
      "family_id": "315",
      "discipline": "Topology",
      "title": "The Singer conjecture in dimension four",
      "pdf_path": "preprints/The-Singer-conjecture-in-dimension-four-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Singer-conjecture-in-dimension-four-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "316:The-Stable-Hurewicz-Image-of-the-Sphere-at-Two-September-25-2026",
      "family_id": "316",
      "discipline": "Topology",
      "title": "The Stable Hurewicz Image of the Sphere at Two",
      "pdf_path": "preprints/The-Stable-Hurewicz-Image-of-the-Sphere-at-Two-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Stable-Hurewicz-Image-of-the-Sphere-at-Two-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "317:Thomason-Model-Structures-in-Every-Strict-Higher-Dimension-September-25-2026",
      "family_id": "317",
      "discipline": "Topology",
      "title": "Thomason Model Structures in Every Strict Higher Dimension",
      "pdf_path": "preprints/Thomason-Model-Structures-in-Every-Strict-Higher-Dimension-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Thomason-Model-Structures-in-Every-Strict-Higher-Dimension-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/317.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "318:Filtered-chromatic-splitting-at-generic-primes-September-25-2026",
      "family_id": "318",
      "discipline": "Topology",
      "title": "Filtered chromatic splitting at generic primes",
      "pdf_path": "preprints/Filtered-chromatic-splitting-at-generic-primes-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Filtered-chromatic-splitting-at-generic-primes-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "318:The-height-three-chromatic-overlap-an-explicit-filtration-and-its-attachments-September-27-2026",
      "family_id": "318",
      "discipline": "Topology",
      "title": "The height-three chromatic overlap: an explicit filtration and its attachments",
      "pdf_path": "preprints/The-height-three-chromatic-overlap-an-explicit-filtration-and-its-attachments-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-height-three-chromatic-overlap-an-explicit-filtration-and-its-attachments-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "318:A-rational-obstruction-to-strong-chromatic-splitting-at-height-three-September-25-2026",
      "family_id": "318",
      "discipline": "Topology",
      "title": "A rational obstruction to strong chromatic splitting at height three",
      "pdf_path": "preprints/A-rational-obstruction-to-strong-chromatic-splitting-at-height-three-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-rational-obstruction-to-strong-chromatic-splitting-at-height-three-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "318:Failure-of-finite-assembly-for-a-chromatic-overlap-at-the-prime-three-September-25-2026",
      "family_id": "318",
      "discipline": "Topology",
      "title": "Failure of finite assembly for a chromatic overlap at the prime three",
      "pdf_path": "preprints/Failure-of-finite-assembly-for-a-chromatic-overlap-at-the-prime-three-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Failure-of-finite-assembly-for-a-chromatic-overlap-at-the-prime-three-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "318:Counterexamples-to-weak-chromatic-splitting-sphere-kernels-and-descent-exponents-September-27-2026",
      "family_id": "318",
      "discipline": "Topology",
      "title": "Counterexamples to weak chromatic splitting: sphere kernels and descent exponents",
      "pdf_path": "preprints/Counterexamples-to-weak-chromatic-splitting-sphere-kernels-and-descent-exponents-September-27-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Counterexamples-to-weak-chromatic-splitting-sphere-kernels-and-descent-exponents-September-27-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "319:Counterexamples-to-the-Hahn-Wilson-conjecture-at-height-two-September-26-2026",
      "family_id": "319",
      "discipline": "Topology",
      "title": "Counterexamples to the Hahn-Wilson conjecture at height two",
      "pdf_path": "preprints/Counterexamples-to-the-Hahn-Wilson-conjecture-at-height-two-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Counterexamples-to-the-Hahn-Wilson-conjecture-at-height-two-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "320:Nonhomeomorphic-closed-aspherical-four-manifolds-with-the-same-homotopy-type-October-4-2026",
      "family_id": "320",
      "discipline": "Topology",
      "title": "Nonhomeomorphic closed aspherical four-manifolds with the same homotopy type",
      "pdf_path": "preprints/Nonhomeomorphic-closed-aspherical-four-manifolds-with-the-same-homotopy-type-October-4-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nonhomeomorphic-closed-aspherical-four-manifolds-with-the-same-homotopy-type-October-4-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "321:A-Counterexample-to-Walls-D2-Problem-October-6-2026",
      "family_id": "321",
      "discipline": "Topology",
      "title": "A Counterexample to Wall's D(2) Problem",
      "pdf_path": "preprints/A-Counterexample-to-Walls-D2-Problem-October-6-2026/wall-d2-counterexample.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Counterexample-to-Walls-D2-Problem-October-6-2026/wall-d2-counterexample.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "322:A-positive-solution-to-Tingleys-problem-September-23-2026",
      "family_id": "322",
      "discipline": "Functional analysis",
      "title": "A positive solution to Tingley\u2019s problem",
      "pdf_path": "preprints/A-positive-solution-to-Tingleys-problem-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-positive-solution-to-Tingleys-problem-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/322.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "323:Relative-independence-of-the-separable-quotient-problem-September-23-2026",
      "family_id": "323",
      "discipline": "Functional analysis",
      "title": "Relative independence of the separable quotient problem",
      "pdf_path": "preprints/Relative-independence-of-the-separable-quotient-problem-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Relative-independence-of-the-separable-quotient-problem-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/323.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "324:Lipschitz-Equivalent-Separable-Banach-Spaces-Need-Not-Be-Linearly-Isomorphic-September-24-2026",
      "family_id": "324",
      "discipline": "Functional analysis",
      "title": "Lipschitz Equivalent Separable Banach Spaces Need Not Be Linearly Isomorphic",
      "pdf_path": "preprints/Lipschitz-Equivalent-Separable-Banach-Spaces-Need-Not-Be-Linearly-Isomorphic-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Lipschitz-Equivalent-Separable-Banach-Spaces-Need-Not-Be-Linearly-Isomorphic-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/324.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "324:Bi-Lipschitz-Absorption-of-c0-Without-a-Linear-Copy-of-c0-September-26-2026",
      "family_id": "324",
      "discipline": "Functional analysis",
      "title": "Bi-Lipschitz Absorption of c0 Without a Linear Copy of c0",
      "pdf_path": "preprints/Bi-Lipschitz-Absorption-of-c0-Without-a-Linear-Copy-of-c0-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Bi-Lipschitz-Absorption-of-c0-Without-a-Linear-Copy-of-c0-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/324.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "325:A-direct-proof-of-the-complete-Crouzeix-inequality-September-26-2026",
      "family_id": "325",
      "discipline": "Functional analysis",
      "title": "A direct proof of the complete Crouzeix inequality",
      "pdf_path": "preprints/A-direct-proof-of-the-complete-Crouzeix-inequality-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-direct-proof-of-the-complete-Crouzeix-inequality-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/A-direct-proof-of-the-complete-Crouzeix-inequality-September-26-2026/build/main.tex",
          "extent": "entire 623-line main TeX source including appendix",
          "sha256": "54a429fe7129b4760b3015fabf2269d4de5fa38aba9539b18542c1df7e58333f",
          "note": "All main argument text read; referenced figure/bibliography, full imported proof, companion structural manuscript and independent acceptance uncompleted."
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/325.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "325:The-complete-Crouzeix-theorem-September-23-2026",
      "family_id": "325",
      "discipline": "Functional analysis",
      "title": "The complete Crouzeix theorem: optimal similarity and a common positive boundary representation",
      "pdf_path": "preprints/The-complete-Crouzeix-theorem-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-complete-Crouzeix-theorem-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/325.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "326:The-cotype-cotype-conjecture-under-the-approximation-property-September-23-2026",
      "family_id": "326",
      "discipline": "Functional analysis",
      "title": "The cotype\u2013cotype conjecture under the approximation property",
      "pdf_path": "preprints/The-cotype-cotype-conjecture-under-the-approximation-property-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-cotype-cotype-conjecture-under-the-approximation-property-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/326.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "327:Nontrivial-Markov-Type-Forces-Superreflexivity-September-23-2026",
      "family_id": "327",
      "discipline": "Functional analysis",
      "title": "Nontrivial Markov Type Forces Superreflexivity",
      "pdf_path": "preprints/Nontrivial-Markov-Type-Forces-Superreflexivity-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nontrivial-Markov-Type-Forces-Superreflexivity-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/327.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "328:Fixed-Points-of-Nonexpansive-Maps-in-Reflexive-Banach-Spaces-September-24-2026",
      "family_id": "328",
      "discipline": "Functional analysis",
      "title": "Fixed Points of Nonexpansive Maps in Reflexive Banach Spaces",
      "pdf_path": "preprints/Fixed-Points-of-Nonexpansive-Maps-in-Reflexive-Banach-Spaces-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Fixed-Points-of-Nonexpansive-Maps-in-Reflexive-Banach-Spaces-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/328.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "329:Counterexamples-to-the-duality-conjecture-for-metric-entropy-September-24-2026",
      "family_id": "329",
      "discipline": "Functional analysis",
      "title": "Counterexamples to the duality conjecture for metric entropy",
      "pdf_path": "preprints/Counterexamples-to-the-duality-conjecture-for-metric-entropy-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Counterexamples-to-the-duality-conjecture-for-metric-entropy-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/329.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "330:Failure-of-Bounded-Approximation-in-a-Lipschitz-Free-Space-over-a-Uniformly-Discrete-Metric-Space-September-26-2026",
      "family_id": "330",
      "discipline": "Functional analysis",
      "title": "A uniformly discrete counterexample to bounded approximation in Lipschitz-free spaces",
      "pdf_path": "preprints/Failure-of-Bounded-Approximation-in-a-Lipschitz-Free-Space-over-a-Uniformly-Discrete-Metric-Space-September-26-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Failure-of-Bounded-Approximation-in-a-Lipschitz-Free-Space-over-a-Uniformly-Discrete-Metric-Space-September-26-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/330.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "331:Asymptotic-midpoint-uniform-convexity-and-unbounded-diamond-distortion-in-a-reflexive-tree-space-September-27-2026",
      "family_id": "331",
      "discipline": "Functional analysis",
      "title": "Asymptotic midpoint uniform convexity and unbounded diamond distortion in a reflexive tree space",
      "pdf_path": "preprints/Asymptotic-midpoint-uniform-convexity-and-unbounded-diamond-distortion-in-a-reflexive-tree-space-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Asymptotic-midpoint-uniform-convexity-and-unbounded-diamond-distortion-in-a-reflexive-tree-space-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/331.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "331:Midpoint-lenses-in-segment-spaces-September-27-2026",
      "family_id": "331",
      "discipline": "Functional analysis",
      "title": "Midpoint lenses in segment spaces",
      "pdf_path": "preprints/Midpoint-lenses-in-segment-spaces-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Midpoint-lenses-in-segment-spaces-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/331.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "331:Diamond-distortion-from-midpoint-and-tree-energies-September-27-2026",
      "family_id": "331",
      "discipline": "Functional analysis",
      "title": "Distortion of countably branching diamonds from midpoint and tree energies",
      "pdf_path": "preprints/Diamond-distortion-from-midpoint-and-tree-energies-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Diamond-distortion-from-midpoint-and-tree-energies-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/331.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "331:Exact-asymptotic-moduli-in-a-Daugavet-subspace-of-L1-September-27-2026",
      "family_id": "331",
      "discipline": "Functional analysis",
      "title": "Exact asymptotic moduli in a Daugavet subspace of L1",
      "pdf_path": "preprints/Exact-asymptotic-moduli-in-a-Daugavet-subspace-of-L1-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-asymptotic-moduli-in-a-Daugavet-subspace-of-L1-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/331.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "331:Midpoint-convexity-from-bounded-tree-potentials-and-path-costs-September-27-2026",
      "family_id": "331",
      "discipline": "Functional analysis",
      "title": "Midpoint convexity from bounded tree potentials and path costs",
      "pdf_path": "preprints/Midpoint-convexity-from-bounded-tree-potentials-and-path-costs-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Midpoint-convexity-from-bounded-tree-potentials-and-path-costs-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/331.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "331:Independent-products-in-real-L1-asymptotic-midpoint-convexity-without-AUC-renormings-September-27-2026",
      "family_id": "331",
      "discipline": "Functional analysis",
      "title": "Independent products in real L1: asymptotic midpoint convexity without AUC renormings",
      "pdf_path": "preprints/Independent-products-in-real-L1-asymptotic-midpoint-convexity-without-AUC-renormings-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Independent-products-in-real-L1-asymptotic-midpoint-convexity-without-AUC-renormings-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/331.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "331:Midpoint-convexity-from-two-recursive-potentials-September-27-2026",
      "family_id": "331",
      "discipline": "Functional analysis",
      "title": "Midpoint convexity from two recursive potentials",
      "pdf_path": "preprints/Midpoint-convexity-from-two-recursive-potentials-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Midpoint-convexity-from-two-recursive-potentials-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/331.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "332:Metric-Markov-Cotype-Two-of-l1-October-5-2026",
      "family_id": "332",
      "discipline": "Functional analysis",
      "title": "Metric Markov Cotype Two of <i>\u2113</i><sub>1</sub> ",
      "pdf_path": "preprints/Metric-Markov-Cotype-Two-of-l1-October-5-2026/l1-markov-cotype.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Metric-Markov-Cotype-Two-of-l1-October-5-2026/l1-markov-cotype.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "333:Smooth-isometric-immersions-of-closed-surfaces-into-Euclidean-four-space-September-23-2026",
      "family_id": "333",
      "discipline": "Differential geometry",
      "title": "Smooth isometric immersions of closed surfaces into Euclidean four-space",
      "pdf_path": "preprints/Smooth-isometric-immersions-of-closed-surfaces-into-Euclidean-four-space-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Smooth-isometric-immersions-of-closed-surfaces-into-Euclidean-four-space-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/333.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "334:A-Smooth-Metric-with-No-Local-Isometric-Immersion-into-Three-Space-September-24-2026",
      "family_id": "334",
      "discipline": "Differential geometry",
      "title": "A Smooth Metric with No Local Isometric Immersion into Three-Space",
      "pdf_path": "preprints/A-Smooth-Metric-with-No-Local-Isometric-Immersion-into-Three-Space-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Smooth-Metric-with-No-Local-Isometric-Immersion-into-Three-Space-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/334.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "335:An-integral-scalar-curvature-bound-for-real-simplicial-volume-October-5-2026",
      "family_id": "335",
      "discipline": "Differential geometry",
      "title": "An integral scalar curvature bound for real simplicial volume",
      "pdf_path": "preprints/An-integral-scalar-curvature-bound-for-real-simplicial-volume-October-5-2026/v126-proof.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-integral-scalar-curvature-bound-for-real-simplicial-volume-October-5-2026/v126-proof.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "335:Positive-scalar-curvature-forces-rational-inessentiality-September-23-2026",
      "family_id": "335",
      "discipline": "Differential geometry",
      "title": "Positive scalar curvature forces rational inessentiality",
      "pdf_path": "preprints/Positive-scalar-curvature-forces-rational-inessentiality-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Positive-scalar-curvature-forces-rational-inessentiality-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "336:Spectral-scalar-curvature-and-uniform-Urysohn-width-October-5-2026",
      "family_id": "336",
      "discipline": "Differential geometry",
      "title": "Spectral scalar curvature and uniform Urysohn width",
      "pdf_path": "preprints/Spectral-scalar-curvature-and-uniform-Urysohn-width-October-5-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Spectral-scalar-curvature-and-uniform-Urysohn-width-October-5-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "336:Spectral-scalar-curvature-and-Urysohn-width-in-dimension-three-October-5-2026",
      "family_id": "336",
      "discipline": "Differential geometry",
      "title": "Spectral scalar curvature and Urysohn width in dimension three",
      "pdf_path": "preprints/Spectral-scalar-curvature-and-Urysohn-width-in-dimension-three-October-5-2026/spectral-urysohn-three-manifolds.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Spectral-scalar-curvature-and-Urysohn-width-in-dimension-three-October-5-2026/spectral-urysohn-three-manifolds.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "336:Positive-scalar-curvature-and-uniform-codimension-two-width-September-23-2026",
      "family_id": "336",
      "discipline": "Differential geometry",
      "title": "Positive scalar curvature and uniform codimension-two width",
      "pdf_path": "preprints/Positive-scalar-curvature-and-uniform-codimension-two-width-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Positive-scalar-curvature-and-uniform-codimension-two-width-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "337:Generalized-Cartan-Hadamard-isoperimetry-and-Euclidean-equality-rigidity-September-23-2026",
      "family_id": "337",
      "discipline": "Differential geometry",
      "title": "Generalized Cartan\u2013Hadamard isoperimetry and Euclidean equality rigidity",
      "pdf_path": "preprints/Generalized-Cartan-Hadamard-isoperimetry-and-Euclidean-equality-rigidity-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Generalized-Cartan-Hadamard-isoperimetry-and-Euclidean-equality-rigidity-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/337.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "337:Sharp-integral-fillings-in-CAT(0)-spaces-September-23-2026",
      "family_id": "337",
      "discipline": "Differential geometry",
      "title": "Sharp integral fillings in CAT(0) spaces",
      "pdf_path": "preprints/Sharp-integral-fillings-in-CAT(0)-spaces-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Sharp-integral-fillings-in-CAT(0)-spaces-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/337.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "338:Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026",
      "family_id": "338",
      "discipline": "Differential geometry",
      "title": "Uniformization of complete K\u00e4hler manifolds with positive bisectional curvature",
      "pdf_path": "preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "339:Entropy-equality-and-local-symmetry-in-negative-curvature-September-23-2026",
      "family_id": "339",
      "discipline": "Differential geometry",
      "title": "Entropy equality and local symmetry in negative curvature",
      "pdf_path": "preprints/Entropy-equality-and-local-symmetry-in-negative-curvature-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Entropy-equality-and-local-symmetry-in-negative-curvature-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "340:A-counterexample-to-the-nearby-Lagrangian-conjecture-September-23-2026",
      "family_id": "340",
      "discipline": "Differential geometry",
      "title": "A counterexample to the nearby Lagrangian conjecture",
      "pdf_path": "preprints/A-counterexample-to-the-nearby-Lagrangian-conjecture-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-counterexample-to-the-nearby-Lagrangian-conjecture-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "341:Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples-October-7-2026",
      "family_id": "341",
      "discipline": "Differential geometry",
      "title": "Deforming hypersymplectic four-manifolds to hyperk\u00e4hler triples",
      "pdf_path": "preprints/Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples-October-7-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples-October-7-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "342:Taming-implies-compatibility-on-four-manifolds-October-6-2026",
      "family_id": "342",
      "discipline": "Differential geometry",
      "title": "Taming implies compatibility on four-manifolds",
      "pdf_path": "preprints/Taming-implies-compatibility-on-four-manifolds-October-6-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Taming-implies-compatibility-on-four-manifolds-October-6-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/342.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "343:Symplectic-Ball-Packings-in-Higher-Dimensions-September-23-2026",
      "family_id": "343",
      "discipline": "Differential geometry",
      "title": "Symplectic Ball Packings in Higher Dimensions",
      "pdf_path": "preprints/Symplectic-Ball-Packings-in-Higher-Dimensions-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Symplectic-Ball-Packings-in-Higher-Dimensions-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/343.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "344:The-metric-Blaschke-theorem-September-23-2026",
      "family_id": "344",
      "discipline": "Differential geometry",
      "title": "The metric Blaschke theorem",
      "pdf_path": "preprints/The-metric-Blaschke-theorem-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-metric-Blaschke-theorem-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "345:Infinitely-many-closed-geodesic-images-on-every-Riemannian-sphere-September-24-2026",
      "family_id": "345",
      "discipline": "Differential geometry",
      "title": "Infinitely many closed geodesic images on every Riemannian sphere",
      "pdf_path": "preprints/Infinitely-many-closed-geodesic-images-on-every-Riemannian-sphere-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Infinitely-many-closed-geodesic-images-on-every-Riemannian-sphere-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "346:A-Codimension-One-Bound-for-the-Singular-Set-of-a-Stationary-Integral-Varifold-October-5-2026",
      "family_id": "346",
      "discipline": "Differential geometry",
      "title": "A Codimension-One Bound for the Singular Set of a Stationary Integral Varifold",
      "pdf_path": "preprints/A-Codimension-One-Bound-for-the-Singular-Set-of-a-Stationary-Integral-Varifold-October-5-2026/varifold-singular-dimension.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Codimension-One-Bound-for-the-Singular-Set-of-a-Stationary-Integral-Varifold-October-5-2026/varifold-singular-dimension.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "346:Almost-everywhere-regularity-of-stationary-integral-varifolds-September-23-2026",
      "family_id": "346",
      "discipline": "Differential geometry",
      "title": "Almost-everywhere regularity of stationary integral varifolds",
      "pdf_path": "preprints/Almost-everywhere-regularity-of-stationary-integral-varifolds-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Almost-everywhere-regularity-of-stationary-integral-varifolds-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "347:Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-in-Dimension-Twenty-Two-October-5-2026",
      "family_id": "347",
      "discipline": "Differential geometry",
      "title": "Hamiltonian Fixed Points Below the Stable Morse Number in Dimension Twenty-Two",
      "pdf_path": "preprints/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-in-Dimension-Twenty-Two-October-5-2026/hamiltonian-fixed-points-below-stable-morse-number.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-in-Dimension-Twenty-Two-October-5-2026/hamiltonian-fixed-points-below-stable-morse-number.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/347.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "347:Sharpness-of-the-Cyclic-Integral-Floer-Bound-Below-the-Stable-Morse-Number-October-5-2026",
      "family_id": "347",
      "discipline": "Differential geometry",
      "title": "Sharpness of the Cyclic Integral Floer Bound Below the Stable Morse Number",
      "pdf_path": "preprints/Sharpness-of-the-Cyclic-Integral-Floer-Bound-Below-the-Stable-Morse-Number-October-5-2026/sharp-cyclic-integral-floer-bound-below-stable-morse-number.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Sharpness-of-the-Cyclic-Integral-Floer-Bound-Below-the-Stable-Morse-Number-October-5-2026/sharp-cyclic-integral-floer-bound-below-stable-morse-number.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/347.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "347:Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-October-5-2026",
      "family_id": "347",
      "discipline": "Differential geometry",
      "title": "Hamiltonian Fixed Points Below the Stable Morse Number",
      "pdf_path": "preprints/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/347.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "347:A-nondegenerate-counterexample-to-the-Morse-number-Arnold-bound-September-23-2026",
      "family_id": "347",
      "discipline": "Differential geometry",
      "title": "A nondegenerate counterexample to the Morse-number Arnold bound",
      "pdf_path": "preprints/A-nondegenerate-counterexample-to-the-Morse-number-Arnold-bound-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-nondegenerate-counterexample-to-the-Morse-number-Arnold-bound-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/347.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "347:A-degenerate-counterexample-to-the-critical-number-Arnold-bound-September-23-2026",
      "family_id": "347",
      "discipline": "Differential geometry",
      "title": "Three fixed points on the symplectic quadric threefold",
      "pdf_path": "preprints/A-degenerate-counterexample-to-the-critical-number-Arnold-bound-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-degenerate-counterexample-to-the-critical-number-Arnold-bound-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/347.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "348:Zero-Plane-Rigidity-for-Einstein-Four-Manifolds-October-4-2026",
      "family_id": "348",
      "discipline": "Differential geometry",
      "title": "Zero-Plane Rigidity for Einstein Four-Manifolds",
      "pdf_path": "preprints/Zero-Plane-Rigidity-for-Einstein-Four-Manifolds-October-4-2026/einstein-boundary.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Zero-Plane-Rigidity-for-Einstein-Four-Manifolds-October-4-2026/einstein-boundary.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/348.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "348:An-L2-Einstein-Gap-for-Nonnegatively-Curved-Four-Manifolds-October-5-2026",
      "family_id": "348",
      "discipline": "Differential geometry",
      "title": "An L\u00b2 Einstein Gap for Nonnegatively Curved Four-Manifolds",
      "pdf_path": "preprints/An-L2-Einstein-Gap-for-Nonnegatively-Curved-Four-Manifolds-October-5-2026/einstein-gap.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-L2-Einstein-Gap-for-Nonnegatively-Curved-Four-Manifolds-October-5-2026/einstein-gap.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/348.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "348:Positively-curved-Einstein-four-manifolds-September-23-2026",
      "family_id": "348",
      "discipline": "Differential geometry",
      "title": "Positively curved Einstein four-manifolds",
      "pdf_path": "preprints/Positively-curved-Einstein-four-manifolds-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Positively-curved-Einstein-four-manifolds-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/348.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "349:The-Solomon-Yau-least-volume-theorem-September-23-2026",
      "family_id": "349",
      "discipline": "Differential geometry",
      "title": "The Solomon\u2013Yau least-volume theorem",
      "pdf_path": "preprints/The-Solomon-Yau-least-volume-theorem-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Solomon-Yau-least-volume-theorem-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "350:Sharp-nodal-length-on-smooth-surfaces-September-23-2026",
      "family_id": "350",
      "discipline": "Differential geometry",
      "title": "Sharp nodal length on smooth surfaces",
      "pdf_path": "preprints/Sharp-nodal-length-on-smooth-surfaces-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Sharp-nodal-length-on-smooth-surfaces-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/350.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "350:Smooth-counterexamples-to-Yaus-nodal-upper-bound-in-dimensions-three-and-four-September-23-2026",
      "family_id": "350",
      "discipline": "Differential geometry",
      "title": "Smooth counterexamples to Yau's nodal upper bound in dimensions three and four",
      "pdf_path": "preprints/Smooth-counterexamples-to-Yaus-nodal-upper-bound-in-dimensions-three-and-four-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Smooth-counterexamples-to-Yaus-nodal-upper-bound-in-dimensions-three-and-four-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/350.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "350:Power-law-violations-of-Yaus-nodal-upper-bound-September-23-2026",
      "family_id": "350",
      "discipline": "Differential geometry",
      "title": "Power-law violations of Yau's nodal upper bound",
      "pdf_path": "preprints/Power-law-violations-of-Yaus-nodal-upper-bound-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Power-law-violations-of-Yaus-nodal-upper-bound-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/350.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "351:A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026",
      "family_id": "351",
      "discipline": "Differential geometry",
      "title": "A closed Ricci flow with bounded scalar curvature and finite-time curvature blowup",
      "pdf_path": "preprints/A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "351:Bounded-scalar-curvature-and-smooth-extension-of-four-dimensional-Ricci-flow-September-24-2026",
      "family_id": "351",
      "discipline": "Differential geometry",
      "title": "Bounded scalar curvature and smooth extension of four-dimensional Ricci flow",
      "pdf_path": "preprints/Bounded-scalar-curvature-and-smooth-extension-of-four-dimensional-Ricci-flow-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Bounded-scalar-curvature-and-smooth-extension-of-four-dimensional-Ricci-flow-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "351:Path-selection-and-an-elliptic-inequality-on-degenerating-Ricci-flat-trees-September-24-2026",
      "family_id": "351",
      "discipline": "Differential geometry",
      "title": "Path selection and an elliptic inequality on degenerating Ricci-flat trees",
      "pdf_path": "preprints/Path-selection-and-an-elliptic-inequality-on-degenerating-Ricci-flat-trees-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Path-selection-and-an-elliptic-inequality-on-degenerating-Ricci-flat-trees-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "352:A-finite-time-singularity-of-Calabi-flow-on-projective-space-September-24-2026",
      "family_id": "352",
      "discipline": "Differential geometry",
      "title": "A finite-time singularity of Calabi flow on projective space",
      "pdf_path": "preprints/A-finite-time-singularity-of-Calabi-flow-on-projective-space-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-finite-time-singularity-of-Calabi-flow-on-projective-space-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "353:Smooth-Nonquadratic-Affine-Maximal-Graph-in-Dimension-Ten-October-5-2026",
      "family_id": "353",
      "discipline": "Differential geometry",
      "title": "A Smooth Nonquadratic Entire Affine Maximal Graph in Dimension Ten",
      "pdf_path": "preprints/Smooth-Nonquadratic-Affine-Maximal-Graph-in-Dimension-Ten-October-5-2026/affine-maximal-dimension-ten.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Smooth-Nonquadratic-Affine-Maximal-Graph-in-Dimension-Ten-October-5-2026/affine-maximal-dimension-ten.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/353.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "353:The-affine-Bernstein-theorem-in-dimensions-three-through-nine-September-24-2026",
      "family_id": "353",
      "discipline": "Differential geometry",
      "title": "The affine Bernstein theorem in dimensions three through nine",
      "pdf_path": "preprints/The-affine-Bernstein-theorem-in-dimensions-three-through-nine-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-affine-Bernstein-theorem-in-dimensions-three-through-nine-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/353.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "354:The-Isoperimetric-Conjecture-for-the-Cubic-Flat-Three-Torus-September-24-2026",
      "family_id": "354",
      "discipline": "Differential geometry",
      "title": "The Isoperimetric Conjecture for the Cubic Flat Three-Torus",
      "pdf_path": "preprints/The-Isoperimetric-Conjecture-for-the-Cubic-Flat-Three-Torus-September-24-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Isoperimetric-Conjecture-for-the-Cubic-Flat-Three-Torus-September-24-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/354.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "355:Tangent-flow-uniqueness-2026-09-24",
      "family_id": "355",
      "discipline": "Differential geometry",
      "title": "Uniqueness of tangent flows at the first singular time of embedded surface mean-curvature flow",
      "pdf_path": "preprints/Tangent-flow-uniqueness-2026-09-24/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Tangent-flow-uniqueness-2026-09-24/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "356:Giglis-distributional-curvature-characterization-of-Alexandrov-spaces-September-24-2026",
      "family_id": "356",
      "discipline": "Differential geometry",
      "title": "Gigli\u2019s distributional curvature characterization of Alexandrov spaces",
      "pdf_path": "preprints/Giglis-distributional-curvature-characterization-of-Alexandrov-spaces-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Giglis-distributional-curvature-characterization-of-Alexandrov-spaces-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/356.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "356:Weak-Hessian-bounds-along-every-geodesic-in-RCD-spaces-September-24-2026",
      "family_id": "356",
      "discipline": "Differential geometry",
      "title": "Weak Hessian bounds along every geodesic in RCD spaces",
      "pdf_path": "preprints/Weak-Hessian-bounds-along-every-geodesic-in-RCD-spaces-September-24-2026/weak-hessian-geodesics.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weak-Hessian-bounds-along-every-geodesic-in-RCD-spaces-September-24-2026/weak-hessian-geodesics.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/356.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "357:Bi-Lipschitz-Coordinates-at-Regular-Points-of-Noncollapsed-RCD-Spaces-September-25-2026",
      "family_id": "357",
      "discipline": "Differential geometry",
      "title": "Bi-Lipschitz Coordinates at Regular Points of Noncollapsed RCD Spaces",
      "pdf_path": "preprints/Bi-Lipschitz-Coordinates-at-Regular-Points-of-Noncollapsed-RCD-Spaces-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Bi-Lipschitz-Coordinates-at-Regular-Points-of-Noncollapsed-RCD-Spaces-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "358:A-Three-Manifold-Without-Conjugate-Points-and-Without-a-Nonpositively-Curved-Metric-September-24-2026",
      "family_id": "358",
      "discipline": "Differential geometry",
      "title": "A Three-Manifold Without Conjugate Points and Without a Nonpositively Curved Metric",
      "pdf_path": "preprints/A-Three-Manifold-Without-Conjugate-Points-and-Without-a-Nonpositively-Curved-Metric-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Three-Manifold-Without-Conjugate-Points-and-Without-a-Nonpositively-Curved-Metric-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/358.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "359:A-negatively-pinched-Kahler-threefold-without-bounded-holomorphic-coordinates-September-25-2026",
      "family_id": "359",
      "discipline": "Differential geometry",
      "title": "A negatively pinched K\u00e4hler threefold without bounded holomorphic coordinates",
      "pdf_path": "preprints/A-negatively-pinched-Kahler-threefold-without-bounded-holomorphic-coordinates-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-negatively-pinched-Kahler-threefold-without-bounded-holomorphic-coordinates-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/359.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "359:One-sided-negative-sectional-curvature-and-the-holomorphic-Liouville-property-September-25-2026",
      "family_id": "359",
      "discipline": "Differential geometry",
      "title": "One-sided negative sectional curvature and the holomorphic Liouville property",
      "pdf_path": "preprints/One-sided-negative-sectional-curvature-and-the-holomorphic-Liouville-property-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/One-sided-negative-sectional-curvature-and-the-holomorphic-Liouville-property-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/359.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "360:Global-Support-and-Convex-Injectivity-Domains-under-Weak-MTW-September-25-2026",
      "family_id": "360",
      "discipline": "Differential geometry",
      "title": "Global Support and Convex Injectivity Domains under Weak MTW",
      "pdf_path": "preprints/Global-Support-and-Convex-Injectivity-Domains-under-Weak-MTW-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Support-and-Convex-Injectivity-Domains-under-Weak-MTW-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/360.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "360:Uniform-Bi-Holder-Transport-from-Weak-MTW-September-25-2026",
      "family_id": "360",
      "discipline": "Differential geometry",
      "title": "Uniform Bi-Holder Transport from Weak MTW",
      "pdf_path": "preprints/Uniform-Bi-Holder-Transport-from-Weak-MTW-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-Bi-Holder-Transport-from-Weak-MTW-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/360.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "361:A-counterexample-to-integer-degree-harmonic-dimension-comparison-September-25-2026",
      "family_id": "361",
      "discipline": "Differential geometry",
      "title": "A counterexample to integer-degree harmonic dimension comparison",
      "pdf_path": "preprints/A-counterexample-to-integer-degree-harmonic-dimension-comparison-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-counterexample-to-integer-degree-harmonic-dimension-comparison-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/361.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "361:A-Three-Dimensional-Counterexample-to-Integer-Degree-Harmonic-Dimension-Comparison-September-26-2026",
      "family_id": "361",
      "discipline": "Differential geometry",
      "title": "A Three-Dimensional Counterexample to Integer-Degree Harmonic Dimension Comparison",
      "pdf_path": "preprints/A-Three-Dimensional-Counterexample-to-Integer-Degree-Harmonic-Dimension-Comparison-September-26-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Three-Dimensional-Counterexample-to-Integer-Degree-Harmonic-Dimension-Comparison-September-26-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/361.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "362:Global-classical-solutions-of-the-three-dimensional-relativistic-Vlasov-Maxwell-system-September-23-2026",
      "family_id": "362",
      "discipline": "Partial differential equations",
      "title": "Global classical solutions of the three-dimensional relativistic Vlasov\u2013Maxwell system",
      "pdf_path": "preprints/Global-classical-solutions-of-the-three-dimensional-relativistic-Vlasov-Maxwell-system-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-classical-solutions-of-the-three-dimensional-relativistic-Vlasov-Maxwell-system-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/362.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "363:Nonuniqueness-with-local-conservation-for-the-hard-sphere-Boltzmann-equation-October-5-2026",
      "family_id": "363",
      "discipline": "Partial differential equations",
      "title": "Nonuniqueness with local conservation for the hard-sphere Boltzmann equation",
      "pdf_path": "preprints/Nonuniqueness-with-local-conservation-for-the-hard-sphere-Boltzmann-equation-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nonuniqueness-with-local-conservation-for-the-hard-sphere-Boltzmann-equation-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/363.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "363:Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026",
      "family_id": "363",
      "discipline": "Partial differential equations",
      "title": "Nonuniqueness for the periodic hard-sphere Boltzmann equation",
      "pdf_path": "preprints/Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/363.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "364:The-Boltzmann-Grad-limit-for-stable-radial-potentials-on-regular-kinetic-intervals-September-23-2026",
      "family_id": "364",
      "discipline": "Partial differential equations",
      "title": "The Boltzmann\u2013Grad limit for stable radial potentials on regular kinetic intervals",
      "pdf_path": "preprints/The-Boltzmann-Grad-limit-for-stable-radial-potentials-on-regular-kinetic-intervals-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Boltzmann-Grad-limit-for-stable-radial-potentials-on-regular-kinetic-intervals-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "364:Hard-sphere-fluctuations-on-the-regular-Boltzmann-lifespan-September-23-2026",
      "family_id": "364",
      "discipline": "Partial differential equations",
      "title": "Hard-sphere fluctuations on the regular Boltzmann lifespan",
      "pdf_path": "preprints/Hard-sphere-fluctuations-on-the-regular-Boltzmann-lifespan-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Hard-sphere-fluctuations-on-the-regular-Boltzmann-lifespan-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "365:Determination-of-a-metric-and-a-unitary-connection-from-one-boundary-patch-October-5-2026",
      "family_id": "365",
      "discipline": "Partial differential equations",
      "title": "Determination of a metric and a unitary connection from one boundary patch",
      "pdf_path": "preprints/Determination-of-a-metric-and-a-unitary-connection-from-one-boundary-patch-October-5-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Determination-of-a-metric-and-a-unitary-connection-from-one-boundary-patch-October-5-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/365.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "365:Smooth-Anisotropic-Uniqueness-in-the-Calderon-Problem-from-One-Boundary-Patch-September-24-2026",
      "family_id": "365",
      "discipline": "Partial differential equations",
      "title": "Smooth anisotropic uniqueness in the Calder\u00f3n problem from one boundary patch",
      "pdf_path": "preprints/Smooth-Anisotropic-Uniqueness-in-the-Calderon-Problem-from-One-Boundary-Patch-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Smooth-Anisotropic-Uniqueness-in-the-Calderon-Problem-from-One-Boundary-Patch-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/365.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "365:Nonuniqueness-for-Bounded-Measurable-Scalar-Conductivities-in-Three-Dimensions-September-23-2026",
      "family_id": "365",
      "discipline": "Partial differential equations",
      "title": "Nonuniqueness for bounded measurable scalar conductivities in three dimensions",
      "pdf_path": "preprints/Nonuniqueness-for-Bounded-Measurable-Scalar-Conductivities-in-Three-Dimensions-September-23-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nonuniqueness-for-Bounded-Measurable-Scalar-Conductivities-in-Three-Dimensions-September-23-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/365.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "366:Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026",
      "family_id": "366",
      "discipline": "Partial differential equations",
      "title": "Interior regularity of planar Mumford\u2013Shah minimizers",
      "pdf_path": "preprints/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "367:The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026",
      "family_id": "367",
      "discipline": "Partial differential equations",
      "title": "The critical dimension for one-phase Bernoulli minimizers",
      "pdf_path": "preprints/The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026/The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026/The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/367.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "368:Strong-diffeomorphic-approximation-in-three-dimensions-for-1-le-p-le-2-September-24-2026",
      "family_id": "368",
      "discipline": "Partial differential equations",
      "title": "Strong diffeomorphic approximation in three dimensions for 1\u2264p\u22642",
      "pdf_path": "preprints/Strong-diffeomorphic-approximation-in-three-dimensions-for-1-le-p-le-2-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Strong-diffeomorphic-approximation-in-three-dimensions-for-1-le-p-le-2-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "368:Strong-diffeomorphic-approximation-in-three-dimensions-for-p-gt-2-September-24-2026",
      "family_id": "368",
      "discipline": "Partial differential equations",
      "title": "Strong diffeomorphic approximation in three dimensions for p>2",
      "pdf_path": "preprints/Strong-diffeomorphic-approximation-in-three-dimensions-for-p-gt-2-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Strong-diffeomorphic-approximation-in-three-dimensions-for-p-gt-2-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "369:Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026",
      "family_id": "369",
      "discipline": "Partial differential equations",
      "title": "Strict hot spots and absence of interior critical points on smooth simply connected planar domains",
      "pdf_path": "preprints/Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026/main.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026/main.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/369.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "370:The-Subcritical-Henon-Lane-Emden-Conjecture-September-24-2026",
      "family_id": "370",
      "discipline": "Partial differential equations",
      "title": "The Subcritical H\u00e9non\u2013Lane\u2013Emden Conjecture",
      "pdf_path": "preprints/The-Subcritical-Henon-Lane-Emden-Conjecture-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Subcritical-Henon-Lane-Emden-Conjecture-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/370.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "371:Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026",
      "family_id": "371",
      "discipline": "Partial differential equations",
      "title": "Stable self-similar blowup for a supercritical defocusing Schr\u00f6dinger equation on the torus",
      "pdf_path": "preprints/Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026/build/main.tex",
          "extent": "lines 1\u2013190",
          "note": "Abstract, main twelve-dimensional selected-power blowup/open-set result, Gaussian corollary, probability boundary and selected methods; no full profile/spectral certificate verification.",
          "sha256": "226895d4fb9c4574e0b5e0c0903bef5345d62eeec4c4605b13dfb885d088a4fb"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/371.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "372:Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026",
      "family_id": "372",
      "discipline": "Partial differential equations",
      "title": "Global Uniqueness for the Smooth Isotropic Elasticity Inverse Problem",
      "pdf_path": "preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/372.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "373:A-counterexample-to-the-Monge-ansatz-for-the-three-marginal-Coulomb-cost-September-25-2026",
      "family_id": "373",
      "discipline": "Partial differential equations",
      "title": "A counterexample to the Monge ansatz for the three-marginal Coulomb cost",
      "pdf_path": "preprints/A-counterexample-to-the-Monge-ansatz-for-the-three-marginal-Coulomb-cost-September-25-2026/paper.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-counterexample-to-the-Monge-ansatz-for-the-three-marginal-Coulomb-cost-September-25-2026/paper.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/373.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "374:Sharp-One-Third-Stability-of-Brenier-Maps-September-25-2026",
      "family_id": "374",
      "discipline": "Partial differential equations",
      "title": "Sharp One-Third Stability of Brenier Maps",
      "pdf_path": "preprints/Sharp-One-Third-Stability-of-Brenier-Maps-September-25-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Sharp-One-Third-Stability-of-Brenier-Maps-September-25-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "selected_section_reading_recorded",
      "section_reading_evidence": [
        {
          "path": "preprints/Sharp-One-Third-Stability-of-Brenier-Maps-September-25-2026/build/source/sections/introduction.tex",
          "extent": "full introduction",
          "note": "Uniform convex source, fixed compact targets and target-uniform one-third endpoint.",
          "sha256": "73d98e5f63dc7d89b91ccb5f47737458a84a463288651ca83ae02f930c9c8b60"
        },
        {
          "path": "preprints/Sharp-One-Third-Stability-of-Brenier-Maps-September-25-2026/build/source/sections/sharpness.tex",
          "extent": "full three-atom sharpness section",
          "note": "Exact cube affine partitions, target coupling lower witness, W1/W2 distances and map norm.",
          "sha256": "2c1682fe0dc4bd8da5883760a909271382ec2a63ef68e8334b5491bb0985c902"
        },
        {
          "path": "preprints/Sharp-One-Third-Stability-of-Brenier-Maps-September-25-2026/build/source/sections/gradient.tex",
          "extent": "lines 1-135",
          "note": "Coordinate projections and explicit admissible constant; beginning of extension statement, not full extension proof.",
          "sha256": "9ea85375b635fd322e71cb7c87cfc015cff8189b2b64fef3a5dbb7a12abba377"
        }
      ],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/374.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "375:De-Giorgis-conjecture-in-dimension-eight-September-26-2026",
      "family_id": "375",
      "discipline": "Partial differential equations",
      "title": "A positive resolution of De Giorgi's conjecture in dimension eight",
      "pdf_path": "preprints/De-Giorgis-conjecture-in-dimension-eight-September-26-2026/article.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/De-Giorgis-conjecture-in-dimension-eight-September-26-2026/article.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "376:Finite-Instructions-and-Solenoidal-Shear-Flows-September-27-2026",
      "family_id": "376",
      "discipline": "Partial differential equations",
      "title": "Finite Instructions and Solenoidal Shear Flows",
      "pdf_path": "preprints/Finite-Instructions-and-Solenoidal-Shear-Flows-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-Instructions-and-Solenoidal-Shear-Flows-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/376.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "376:A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026",
      "family_id": "376",
      "discipline": "Partial differential equations",
      "title": "A Fixed Particle Test for Computation in a Forced Viscous Flow",
      "pdf_path": "preprints/A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/376.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "376:Universal-Computation-with-Eventually-Stationary-Navier-Stokes-Forcing-September-27-2026",
      "family_id": "376",
      "discipline": "Partial differential equations",
      "title": "Universal Computation with Eventually Stationary Navier\u2013Stokes Forcing",
      "pdf_path": "preprints/Universal-Computation-with-Eventually-Stationary-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Universal-Computation-with-Eventually-Stationary-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/376.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "376:Geometric-Programs-for-Solenoidal-Forcing-September-27-2026",
      "family_id": "376",
      "discipline": "Partial differential equations",
      "title": "Geometric Programs for Solenoidal Forcing",
      "pdf_path": "preprints/Geometric-Programs-for-Solenoidal-Forcing-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Geometric-Programs-for-Solenoidal-Forcing-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/376.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "376:Prefix-Instructions-and-Incompressible-Flows-September-27-2026",
      "family_id": "376",
      "discipline": "Partial differential equations",
      "title": "Prefix Instructions and Incompressible Flows",
      "pdf_path": "preprints/Prefix-Instructions-and-Incompressible-Flows-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Prefix-Instructions-and-Incompressible-Flows-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/376.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "376:Computation-under-Rapidly-Vanishing-Navier-Stokes-Forcing-September-27-2026",
      "family_id": "376",
      "discipline": "Partial differential equations",
      "title": "Computation under Rapidly Vanishing Navier\u2013Stokes Forcing",
      "pdf_path": "preprints/Computation-under-Rapidly-Vanishing-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Computation-under-Rapidly-Vanishing-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/376.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "376:Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026",
      "family_id": "376",
      "discipline": "Partial differential equations",
      "title": "Velocity-Field Detection of Computation in Forced Navier\u2013Stokes Flows",
      "pdf_path": "preprints/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/376.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "376:Scalar-Potentials-and-Slow-Clocks-for-Forced-Fluid-Computation-September-27-2026",
      "family_id": "376",
      "discipline": "Partial differential equations",
      "title": "Scalar Potentials and Slow Clocks for Forced Fluid Computation",
      "pdf_path": "preprints/Scalar-Potentials-and-Slow-Clocks-for-Forced-Fluid-Computation-September-27-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Scalar-Potentials-and-Slow-Clocks-for-Forced-Fluid-Computation-September-27-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/376.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "376:Incompressible-Box-Transport-and-Finite-Computation-October-6-2026",
      "family_id": "376",
      "discipline": "Partial differential equations",
      "title": "Incompressible Box Transport and Finite Computation",
      "pdf_path": "preprints/Incompressible-Box-Transport-and-Finite-Computation-October-6-2026/manuscript.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Incompressible-Box-Transport-and-Finite-Computation-October-6-2026/manuscript.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": "lean/docs/376.md",
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    },
    {
      "manuscript_id": "377:Uniform-Interior-C1alpha-Estimates-for-Infinity-Harmonic-Functions-October-4-2026",
      "family_id": "377",
      "discipline": "Partial differential equations",
      "title": "Uniform Interior $`C^{1,\\alpha}`$ Estimates for Infinity-Harmonic Functions",
      "pdf_path": "preprints/Uniform-Interior-C1alpha-Estimates-for-Infinity-Harmonic-Functions-October-4-2026/interior-c1-infinity-harmonic.pdf",
      "pdf_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-Interior-C1alpha-Estimates-for-Infinity-Harmonic-Functions-October-4-2026/interior-c1-infinity-harmonic.pdf",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "pdf_present": true,
      "review_status": "earlier_notes_not_imported_or_individual_review_pending",
      "section_reading_evidence": [],
      "full_manuscript_review_complete": false,
      "independent_proof_verification": "not_run",
      "selected_family_scope_document": null,
      "interpretation": "A family review or scope document does not certify every companion manuscript. No section record here does not establish that the paper was never previously consulted."
    }
  ],
  "counts": {
    "earlier_notes_not_imported_or_individual_review_pending": 683,
    "selected_section_reading_recorded": 36
  },
  "total": 719,
  "scope": "36 selected-section records with 86 source hashes; 683 earlier-notes-not-imported or individually pending. Full proof/source acceptance remains incomplete."
}
