{
  "report_received_on": "2026-11-05",
  "source": "Independent mathematical audit report supplied by the user.",
  "reviewer_name": null,
  "reviewer_model": null,
  "reviewer_type": null,
  "audit_completion_date": null,
  "identity_scope": "Reviewer identity, model, human/model type and completion date were not specified; none is inferred.",
  "report_file": "review/independent-audit-2026-11-05.txt",
  "report_sha256": "53821929bf69694a5c93bef117ee9fc412dde1f1802d9ecc61a48084a38619d1",
  "reported_pdf": "output/pdf/even-beta-counts.pdf",
  "audited_path_snapshot": {
    "pages": 19,
    "pdf_sha256": "55bc50db83f1fa0d254af05e0782b929af102f1423206c642589e5c1e0cddfba",
    "source_files": {
      "paper/even-beta-counts.tex": "b591ba2d484502de8777c283eb42355ab1242de42f4da29c2a69c24c139ecf92",
      "paper/references.tex": "2c860190b9e8972c4e2b7affb01139b117a2569f22af74f72cbffa7f70202f6c",
      "paper/sections/arithmetic.tex": "59fbe3dbcbd49be0f873be522f4b2fda8c09fbf8a2631b9ffed2c8a01eaf3af5",
      "paper/sections/checks.tex": "ccf9b57ad7cfa8cbefbc028a84b8a9e1e2a01ebc363fda697d12bd38c039b0c6",
      "paper/sections/construction.tex": "7fda38775dc1358bf5905e336d236e62f27f6c31f8d5319d2b2e54457c0f79d3",
      "paper/sections/contradiction.tex": "1ef2b638788a99f3f3a64fa8a204e14fa2f424f65e104c3c26b3f1f0b27d761f",
      "paper/sections/count.tex": "cb20704c969dc37db1a9ade6f333999e8efe695da3f9bbc701244970cfabf2de",
      "paper/sections/decay.tex": "190422c9cf259934d4bc57f93f633557df857717e7e1674f70de2f172234fed3",
      "paper/sections/dilation.tex": "c974aa5a16d204e9311c430390249987c87429fd18f53cda45da79162418920e",
      "paper/sections/earlier-count.tex": "b011c10a8dc0503c5d2ba326866edc9c2260aeed4a0a434132745982f205c266",
      "paper/sections/endpoints.tex": "bb9ef16213394604e8e1bde99c8a8ab384440d4d47110a3b10798872de0b20d3",
      "paper/sections/gram.tex": "2d7a07e0fe1994a94061c87e4aab06e9a311d53cc4a6f7b4425401044261d455",
      "paper/sections/introduction.tex": "e9e1c4c36cdd3b6560486c1d1c23cffb3ddc861f87f2256ffc79973541032d23"
    },
    "version_binding": "The report named the canonical PDF path. The PDF snapshot and matching source hashes were captured from that path before the explanatory revision. The reviewer did not supply a checksum.",
    "preserved_privately": true
  },
  "conclusion": "No substantive mathematical error or gap found.",
  "reported_results": {
    "rounded_bound": "I(s) >= floor(pi*sqrt(2/135)*sqrt(s/log(s))) for every even s >= 160.",
    "unrounded_bound": "I(s) >= pi*sqrt(2/135)*sqrt(s/log(s)) for every even s >= 42170."
  },
  "reported_general_arguments_checked": [
    {
      "pages": "5-7",
      "scope": "Gram construction: kernel independence, contour sign and normalization, positivity, convergence, integer homogeneous multiplier and rank for every B."
    },
    {
      "pages": "7-9",
      "scope": "Denominators: progression lemma and grouped cancellation for rational constants."
    },
    {
      "pages": "9-11",
      "scope": "Decay: Stirling normalization, unique maximum, uniform estimates and infinite-tail control."
    },
    {
      "pages": "11-12",
      "scope": "Prime dilation: factorial units, permutation of fraction classes, local Laurent-coefficient extraction and surviving factor chi_4(p)*(m+1)^(-S)."
    },
    {
      "pages": "13-17",
      "scope": "Contradiction and inversion: nonzero Vandermonde minor, infinitely many nonzero cleared integers, ceiling/floor handling and coverage of every claimed endpoint."
    }
  ],
  "reported_independent_method": "Independently written arithmetic; the reviewer reports not running or importing the supplied checkers.",
  "reported_checks": {
    "all_passed": true,
    "rational_gram_entries": 385,
    "positive_leading_principal_minors": 55,
    "integer_seed_vector_identities": 10,
    "finite_endpoint_decay_choices": 10,
    "finite_interval_comparisons": 253,
    "selected_pole_coefficient_congruences": 272,
    "other_pole_valuation_bounds": 2312,
    "constant_congruences": 10,
    "grouped_integrality_checks": 4802,
    "smallest_interval_margins_approximately": [
      "0.0002452910722",
      "0.0001432530917"
    ],
    "infinite_range_rational_constants_passed": true
  },
  "independent_checker_artifacts": "The narrative report was supplied; no independent checker source or machine-readable calculation output was supplied.",
  "recommended_revision": "Explain why the Stirling error remains uniform down to t=1/B, where t/n tends to zero. The report affirms the asserted estimate and requests an exposition improvement.",
  "auditor_changed_files": false,
  "formal_verification": false,
  "fresh_audit_of_all_cited_literature": false,
  "subsequent_revision_record": "review/audit-response-2026-11-05.json"
}