{
  "classification": "local integration validation; no independent review or RH proof",
  "version": "v1.64",
  "date": "2026-09-23",
  "tasks": [
    "NS-81"
  ],
  "publication_base_commit": "c1409f4433fc4e0f56fc4de79e094be0274b74e4",
  "manuscript": {
    "pages": 352,
    "warning_counts": {
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      "underfull_boxes": 0,
      "latex_warnings": 0,
      "pdftex_warnings": 0,
      "duplicate_pdf_destinations": 0
    },
    "proof_fragment_integrated_verbatim_once": true,
    "proof_sha256": "bdedfeca6b9c897955d2c177e034b27d24f7dab1a651f55229b7d0aad7a0248c",
    "main_tex_sha256": "8a966fdf57d03447db5924dc7c513151c419c7af8ea6d7d7fbe4bd9951de772f",
    "pdf_sha256": "2e47774b88df21873e25f8e7bbe465c00077f48b475036b04699f33ec1abd279",
    "new_section_visual_review_pages": [
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  },
  "maxima_exact_checks": {
    "NS-81": 18
  },
  "maxima_total": 18,
  "arb_precisions_bits": [
    256,
    384
  ],
  "replays": {
    "status": "PASS",
    "precision_bits": [
      256,
      384
    ],
    "precision_enclosure_matches": 27,
    "source_sha256": "6872259cfe2269e7c5b32d210b32ccd2f65ff5ede34837b22ba1b3bb5dc358af",
    "prefix_matrices_tested": [
      16,
      64,
      256
    ],
    "complete_scalar_tail_bounds_tested": [
      16,
      64,
      256
    ],
    "enormous_comparators_assembled": false,
    "cutoff_replay": "not applicable: all small prefix cells evaluated; infinite tail bounded by a complete analytic inequality",
    "minimum_serialized_accuracy_bits": 205,
    "cofinal_error_decay": false,
    "independent_review": false
  },
  "python_diagnostics": {
    "errors": 0,
    "warnings": 0,
    "scope": "all new v164 scientific Python"
  },
  "source_sha256": {
    "ns81/certify_conditioning.py": "6872259cfe2269e7c5b32d210b32ccd2f65ff5ede34837b22ba1b3bb5dc358af",
    "ns81/exact-checks.mac": "f055b1cecf06ac2ae5069249f1d3a322b7164894d1a1ada94e80834176913e61",
    "ns81/proof.tex": "bdedfeca6b9c897955d2c177e034b27d24f7dab1a651f55229b7d0aad7a0248c",
    "proof.tex": "bdedfeca6b9c897955d2c177e034b27d24f7dab1a651f55229b7d0aad7a0248c",
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  "independent_review": false,
  "open_inputs": [
    "Cofinal decay of the complete signed arithmetic sample sum",
    "Available block gain relative to the entire residual energy",
    "Practical application of the arithmetic sampling comparator",
    "Original arithmetic Weil floor, API, G2 and RH"
  ],
  "limits": [
    "The conditioning bound concerns ordinary positive integer Grams, not signed Weil forms",
    "Only the small finite-prefix matrices at N16,64,256 were assembled",
    "The discarded infinite sample tail is bounded analytically, not truncated silently",
    "The enormous finite comparator was not assembled",
    "The sufficient cutoff uses the total atom count, including both old and new atoms",
    "The displayed cutoff is sufficient, not necessary or a complexity lower bound",
    "The stronger inverse-trace check is only asserted at the tested finite sizes",
    "Polynomial conditioning does not give cofinal approximation-error decay"
  ],
  "publication_authorization": "User requested PRs and subsequently explicitly allowed validated merges and version tags.",
  "html_checks": {
    "balanced_nesting": true,
    "local_links_resolve": true,
    "inline_styles_only": true,
    "browser_visual_review": false,
    "preview": "Codex file preview; prior local browser restriction respected"
  }
}