{
  "received_at_utc": "2026-11-06T17:56:45.779111+00:00",
  "source": "Independent audit report supplied by the user in this conversation.",
  "auditor_identity": null,
  "auditor_model": null,
  "separate_audit_date": null,
  "audited_file": "Plain-text proof preserved locally; SHA-256 identifies the audited snapshot.",
  "audited_sha256": "603211b50609dc4a4f6646815e7192b61bb8d264c93868d39921f1e0843454e7",
  "reported_sha256_prefix": "603211b50609dc4a",
  "hash_match_verified": true,
  "result": "Theorems A and B pass; no substantive gap or mathematical repair identified.",
  "scope": [
    "General Gram construction and rank",
    "Denominator clearing",
    "Analytic decay and endpoint criterion",
    "Prime dilation, elimination and contradiction",
    "Uniform bounds and exact finite certificates"
  ],
  "checker_independence": {
    "source_inspected_for_coverage": true,
    "supplied_checkers_run_or_imported": false,
    "independently_written_calculations": true
  },
  "independent_methods": [
    "Rational interpolation from direct kernel evaluations",
    "Logarithmic-derivative Taylor recurrence for pole coefficients",
    "Separate moment recurrence for Gram integrals"
  ],
  "structural_checks": {
    "total": 8909,
    "categories": {
      "kernel_evaluations": 57,
      "gram_entries": 49,
      "positive_principal_minors": 19,
      "seed_targets": 9,
      "reconstructions": 54,
      "reflection_coefficients": 1308,
      "differentiated_grid_zeros": 332,
      "grouped_integrality": 4516,
      "selected_pole_congruences": 404,
      "other_pole_bounds": 1940,
      "constant_congruences": 19,
      "beta_coefficient_bounds": 202
    }
  },
  "endpoint_certificates": 21,
  "uniform_parameter_records": 6,
  "integer_r_exclusions": 7,
  "tightest_listed_endpoint": {
    "B": 10,
    "m": 3,
    "a": 8382,
    "U_approx": "0.991303468061"
  },
  "limiting_endpoint_multiplier_approx": "18.5722528999226532907",
  "exposition_recommendations": [
    "Worked B=2,m=1 Gram example",
    "Explicit coefficient scaling from (5.2) to (5.3)"
  ],
  "report_file": "review/independent-audit-2026-11-06.txt",
  "formal_verification_reported": false,
  "post_audit_exposition": {
    "manuscript": "paper/shifted-even-beta.tex",
    "original_audited_file_preserved": true,
    "theorem_statements_unchanged": true,
    "separate_independent_audit": false,
    "new_example_exact_self_check": "checks/worked_example.json",
    "assembly_record": "review/assembly-review.json"
  }
}