{
  "title": "Exact supporting checks for Linear independence of even Dirichlet beta values",
  "source_repository": "https://github.com/twinheterodox/beta4",
  "source_commit": "85da9e50077215aa63f7ebe1eba5a8513b3f0f6c",
  "source_directory": "even-beta-independence/checks",
  "dependency": {
    "name": "sympy",
    "version": "1.14.0"
  },
  "run_from": "The root of the extracted submission archive",
  "commands": [
    "python3 -m pip install sympy==1.14.0",
    "python3 anc/check_local_system.py",
    "python3 anc/check_linear_forms.py"
  ],
  "outputs": {
    "anc/check_local_system.py": "anc/local-system-results.json",
    "anc/check_linear_forms.py": "anc/half-shift-forms-checks.json"
  },
  "expected_report_sha256": {
    "anc/local-system-results.json": "8643a52cb8421f8082745209b0fb8b051c9e656703a08978214f75a08e51790a",
    "anc/half-shift-forms-checks.json": "22a845d2a459882d32e1f3ceb308338c0e307c8eba13bc5fa5cebd295c3b5806"
  },
  "coverage": [
    "52 exact distinct-product least-common-multiple comparisons.",
    "2304 exact Taylor-coefficient comparisons, including 1204 nonzero coefficients, at depth 7 through order 36; denominator checks for all tested coefficients.",
    "100 enlarged-system symbolic identities, three quadratic-pullback and residue checks, and 12 descending-residue identities.",
    "Exact rational certificates that the limiting constant exceeds 0.21 and the rank-inequality slope exceeds 1.",
    "Six linear-form coefficient vectors compared through partial fractions and differential-system recurrences."
  ],
  "limitations": "These finite exact checks support the written proof. They do not establish the asymptotic theorem, prove the general denominator or multiplicity statements, or constitute formal verification. One coefficient fixture is zero; the proof requires a weak rank condition on families, not nonvanishing of every row.",
  "preparation": "Scripts prepared and checked by the developing Codex assistant; the separate AI-model cross-check concerned the paper.",
  "packaging": "The two scripts and their reference reports are unchanged from the public repository. Only their containing directory changes from checks/ to anc/."
}