{
  "reported_on": "2026-11-05",
  "provenance": "Report supplied by the user in this conversation; independent checker code not supplied here.",
  "auditor_identity": null,
  "auditor_model": null,
  "separate_audit_date": null,
  "reported_sha256_prefix": "c7197fc5cd341c3c",
  "audited_proof_sha256": "c7197fc5cd341c3cb71ab30515be836f2cea0156b1252284229bd8d059cdf258",
  "audited_proof_snapshot": "Preserved privately; the SHA-256 identifies the audited input.",
  "report": "review/independent-audit-2026-11-05.txt",
  "conclusion": "No substantive mathematical error or gap; general shifted-interval theorem survives the audit.",
  "scope": "General arguments for arbitrary allowed parameters, including differentiated Gram rank, denominators, derivative decay, prime dilation, contradiction and endpoints.",
  "independent_computation": "Reported independently written code, without running or importing supplied checkers.",
  "reproduced_checks": {
    "kernel_evaluations": 120,
    "Gram_entries": 90,
    "positive_principal_minors": 30,
    "integer_seed_vectors": 12,
    "selected_pole_congruences": 800,
    "other_pole_bounds": 6800,
    "constant_congruences": 14,
    "grouped_integrality_seed_and_prime": 6564,
    "displayed_interval_certificates": 4,
    "universal_endpoint_rational_inequalities": "All passed"
  },
  "additional_dilation_case": {
    "seed_index": 3,
    "prime": 17,
    "n": 51,
    "coefficient_and_constant_congruences": "Passed, as reported; remaining parameters not specified."
  },
  "wording_correction": {
    "audited_line": 490,
    "before": "its numerator or denominator",
    "after": "the numerator or denominator of q_w(1)",
    "applied": true
  },
  "post_audit_proof_changes": [
    "Status note records the audit and identifies the archived version.",
    "Ambiguous pronoun in the prime exclusion is replaced by q_w(1)."
  ],
  "mathematical_argument_unchanged": true,
  "limitations": "Independent mathematical audit, not formal verification or certification of priority.",
  "manuscript_scope": "The independent audit applies to the underlying plain-text proof, not this subsequently assembled PDF. The mathematical correspondence, exact checks and visual review of the LaTeX manuscript are recorded in review/assembly-review.json."
}