{
  "family_id": "227",
  "title": "Critical SK autocorrelation processes and dynamics across the temperature transition",
  "discipline": "Probability and statistical mechanics",
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "papers": [
    {
      "title": "Universality of critical quench autocorrelations in the Sherrington–Kirkpatrick model",
      "path": "preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/main.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",
      "readme_path": "preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Functional universality of critical SK autocorrelations",
      "path": "preprints/Functional-universality-of-critical-SK-autocorrelations-October-5-2026/critical-sk-autocorrelations.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Functional-universality-of-critical-SK-autocorrelations-October-5-2026/critical-sk-autocorrelations.pdf",
      "readme_path": "preprints/Functional-universality-of-critical-SK-autocorrelations-October-5-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "A spectral gap throughout the high-temperature Sherrington–Kirkpatrick phase",
      "path": "preprints/A-spectral-gap-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026/main.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",
      "readme_path": "preprints/A-spectral-gap-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Cutoff throughout the high-temperature Sherrington–Kirkpatrick phase",
      "path": "preprints/Cutoff-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Cutoff-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026/paper.pdf",
      "readme_path": "preprints/Cutoff-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Critical slowing down in the Sherrington–Kirkpatrick model",
      "path": "preprints/Critical-slowing-down-in-the-Sherrington-Kirkpatrick-model-September-24-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Critical-slowing-down-in-the-Sherrington-Kirkpatrick-model-September-24-2026/paper.pdf",
      "readme_path": "preprints/Critical-slowing-down-in-the-Sherrington-Kirkpatrick-model-September-24-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Stretched-exponential barriers for typical SK initial states",
      "path": "preprints/Stretched-exponential-barriers-for-typical-SK-initial-states-September-24-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Stretched-exponential-barriers-for-typical-SK-initial-states-September-24-2026/paper.pdf",
      "readme_path": "preprints/Stretched-exponential-barriers-for-typical-SK-initial-states-September-24-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "A typical-start upper bound for low-temperature SK Glauber dynamics",
      "path": "preprints/A-typical-start-upper-bound-for-low-temperature-SK-Glauber-dynamics-September-24-2026/paper.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",
      "readme_path": "preprints/A-typical-start-upper-bound-for-low-temperature-SK-Glauber-dynamics-September-24-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Critical mixing in the Sherrington–Kirkpatrick model",
      "path": "preprints/Critical-mixing-in-the-Sherrington-Kirkpatrick-model-September-25-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Critical-mixing-in-the-Sherrington-Kirkpatrick-model-September-25-2026/paper.pdf",
      "readme_path": "preprints/Critical-mixing-in-the-Sherrington-Kirkpatrick-model-September-25-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    }
  ],
  "lean_scope_path": "lean/docs/227.md",
  "lean_scope_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/227.md",
  "verification_status": "scope_document_available_not_independently_verified",
  "review_status": "inventory_complete_deep_review_pending"
}