{
  "family_id": "154",
  "title": "Pointwise multiple ergodic averages for mixing transformations",
  "discipline": "Dynamical systems and ergodic theory",
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "papers": [
    {
      "title": "Pointwise Multiple Ergodic Averages for Mixing Transformations",
      "path": "preprints/Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026/multiple-ergodic-averages.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026/multiple-ergodic-averages.pdf",
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    },
    {
      "title": "Pointwise convergence of fourfold ergodic averages for mixing transformations",
      "path": "preprints/Pointwise-convergence-of-fourfold-ergodic-averages-for-mixing-transformations-October-4-2026/fourfold-ergodic-averages.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",
      "readme_path": "preprints/Pointwise-convergence-of-fourfold-ergodic-averages-for-mixing-transformations-October-4-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Triple ergodic averages with distinct integer slopes",
      "path": "preprints/Triple-ergodic-averages-with-distinct-integer-slopes-October-4-2026/triple-ergodic-distinct-slopes.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",
      "readme_path": "preprints/Triple-ergodic-averages-with-distinct-integer-slopes-October-4-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Pointwise convergence of triple ergodic averages for mixing transformations",
      "path": "preprints/Pointwise-convergence-of-triple-ergodic-averages-for-mixing-transformations-October-4-2026/pointwise-triple-ergodic-averages-mixing-transformations.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",
      "readme_path": "preprints/Pointwise-convergence-of-triple-ergodic-averages-for-mixing-transformations-October-4-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    }
  ],
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  "lean_scope_url": null,
  "verification_status": "no_family_scope_document",
  "review_status": "inventory_complete_deep_review_pending"
}