{
  "title": "Independent model proof audit of the 19-page manuscript",
  "reported_on": "2026-11-03",
  "source_commit": "095d309ae168757dbfa4063484d28186f7f41beb",
  "source_record_url": "https://github.com/twinheterodox/beta4/tree/095d309ae168757dbfa4063484d28186f7f41beb/even-beta-independence/review/independent-model-review-2026-11-03.json",
  "source_report_url": "https://github.com/twinheterodox/beta4/tree/095d309ae168757dbfa4063484d28186f7f41beb/even-beta-independence/review/independent-model-review-2026-11-03.txt",
  "source_report_sha256": "87e4586251bd9a1786d2924229302a92009d38c5af9367bba63031fe7c991899",
  "supplied_report_verbatim": "INDEPENDENT MODEL PROOF AUDIT\nReported by the author on 3 November 2026.\nReviewer: a second model; its name and review execution date were not supplied.\nScope and reviewed revision: independent-model-review-2026-11-03.json.\n\nUser-supplied report (verbatim)\n\na second model: I found no substantive mathematical gap in the current 19-page version. The revisions also make the argument considerably easier to follow.\n\n  The critical checks hold up:\n\n  • Denominators (§4): successive integrations produce distinct denominator factors, justifying the harmonic-number cost.\n  • Rank (§6): the common polynomial row, residue argument, and counting at all six points fit together. The application of Fischler’s multiplicity estimate meets its stated hypotheses.\n  • Final bound (§7): the parameter constraints and passage to all sufficiently large even s work. I recomputed\n    c_{*} = 0.217456234803943567… > 0.21.\n\n  All supplied exact checks passed. Separate checks also passed through Taylor degree 60 and depth 12, alongside numerical checks of the tail identities.\n\n  The new two-integration example on page 8, the h=1 example on page 13, and the explanation of the infinity contribution substantially improve the exposition.\n\n  No mathematical correction identified in this pass. This remains a proof audit using the cited results, not formal verification; the finite computations support particular identities rather than certify the theorem. I changed no files.\n",
  "scope": [
    "Current 19-page proof, using the cited results.",
    "Section 4: distinct denominator factors from successive integrations and the harmonic-number cost.",
    "Section 6: common polynomial row, residue argument, all six points and the stated hypotheses of Fischler's multiplicity estimate.",
    "Section 7: parameter constraints, passage to all sufficiently large even s and recomputation of the limiting constant.",
    "Supplied exact checks, additional exact checks and numerical tail-identity checks.",
    "Exposition: two-integration example, h=1 common-row example and explanation of the infinity contribution."
  ],
  "reviewer_model": null,
  "formal_verification": false,
  "additional_reviewer_check_code_and_outputs_supplied": false,
  "reviewed_pdf_sha256": "68e78a076de5ecfc59512bb70e4478c3142301564973c5583a51013dd5ee857a",
  "revision_note": "The audit identifies the final 19-page exposition revision before the preparation-note update. The subsequent status update and repository relocation leave the mathematical text unchanged."
}