{
  "classification": "local integration validation; no independent review or RH proof",
  "version": "v1.66",
  "date": "2026-09-23",
  "tasks": [
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    "main_tex_sha256": "8e494729b436099efc41bedf391e7ecf1c4ff7548176ec0692bb2843a6c2aeab",
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  "maxima_exact_checks": {
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  "maxima_total": 33,
  "arb_precisions_bits": [
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  "replays": {
    "status": "PASS",
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    "finite_zero_subset_only": true,
    "cutoff_replay": "not applicable: omitted zero weights are nonnegative and the subset constant is only a lower bound",
    "finite_N_error_bound": false,
    "asymptotic_onset_N0": null,
    "independent_review": false
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  "python_diagnostics": {
    "errors": 0,
    "warnings": 0,
    "scope": "all new v166 scientific Python"
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  "independent_review": false,
  "open_inputs": [
    "Cofinal decay of the actual arithmetic optimal residual",
    "A nonsummable lower estimate on relative arithmetic block gain compatible with the logarithmic budget",
    "Original arithmetic Weil floor, API, G2 and RH"
  ],
  "limits": [
    "Fixed smoothing order only",
    "Asymptotic lower bound, not convergence or an upper estimate",
    "No finite-N onset threshold or pointwise bound on each gain",
    "Certified zero subset gives only a lower bound on the full constant",
    "Classical Burnol mechanism with extra Hardy operators; no new-zero or priority claim",
    "Uniform capture of available block gain remains possible"
  ],
  "literature_inputs": {
    "Burnol": {
      "url": "https://arxiv.org/abs/math/0103058",
      "version": "v2, 20 March 2001; published Advances in Mathematics 170 (2002), 56\u201370",
      "used": "Sections 3\u20135: phase construction, oscillatory-integral expansion before Theorem 4.11, and target identity in Theorem 5.4",
      "adaptation": "Extra Hardy operators, complete uniform endpoint/tail bounds, target pairing and fixed-order critical weight derived in NS83; no new-mechanism priority claim"
    },
    "FLINT": {
      "url": "https://flintlib.org/doc/acb_dirichlet.html",
      "used": "Certified nontrivial zero enclosures via python-flint acb.zeta_zero; only first ten positive ordinates and their conjugates contribute to a subset lower bound"
    },
    "zero_count": {
      "manuscript_key": "HasanalizadeShenWong2021",
      "used": "Unit-height zero count O(log T) and hence convergence of the positive weighted multiplicity series"
    }
  },
  "publication_authorization": "User requested PRs and subsequently explicitly allowed validated merges and version tags.",
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    "browser_visual_review": false,
    "preview": "Codex file preview; prior local browser restriction respected"
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}