{
  "title": "Supporting material for Linear independence of even Dirichlet beta values",
  "intended_hexagon_update": {
    "work": "2611.00044",
    "version": 2,
    "previous_version_url": "https://hexagonmath.org/2611.00044v1"
  },
  "source_repository": "https://github.com/twinheterodox/beta4",
  "source_commit": "095d309ae168757dbfa4063484d28186f7f41beb",
  "source_directory": "even-beta-independence",
  "source_url": "https://github.com/twinheterodox/beta4/tree/095d309ae168757dbfa4063484d28186f7f41beb/even-beta-independence",
  "manuscript": {
    "main_tex_file": "even-beta-independence.tex",
    "compiler": "pdfLaTeX",
    "pages": 19,
    "canonical_pdf_sha256": "83fff93aebeff3b79fb2f316df94518321a7b7dab815c7ab37d8ebf0b5cc5fe8"
  },
  "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."
  ],
  "independent_review": "anc/independent-model-review.json",
  "review_scope": "The second model reported no substantive mathematical gap and further computational checks. Its additional code and outputs were not supplied; the included scripts implement only the coverage listed above.",
  "limitations": "The finite computations support particular identities in the written proof; they do not certify the asymptotic theorem or constitute formal verification.",
  "preparation": "Prepared with OpenAI Codex. The author identifies the exposition model as Astra-6-Max. The independent reviewing model was not named.",
  "packaging": "All manuscript sources, scripts and exact result files come from the pinned public Git commit. Only the eight TeX input paths are changed. This archive contains no build files or private working records."
}