{
  "reviewed_commit": "8545cb8d126aca2576b0fe9c5bb6a047ea09c031",
  "owner_unchanged": true,
  "result": "No mathematical theorem defect or catalog-blocking scope error found; retain translated-model-only interpretation.",
  "checks": [
    {
      "check": "Default algorithm variant",
      "status": "pass",
      "assessment": "Matches exp(median(log-count minus mean-log-count)); even medians average central log values."
    },
    {
      "check": "Model domains",
      "status": "pass",
      "assessment": "Finite real rows, positive sample scales, nonempty all-positive retained rows; production interpretation requires nonnegative finite dense data and at least one sample."
    },
    {
      "check": "Scaling equivariance",
      "status": "pass",
      "assessment": "Exact-real factor c[j]/G(c), with eligibility preserved."
    },
    {
      "check": "Normalized ratios",
      "status": "pass",
      "assessment": "Common G(c) factor cancels; public positive-retained-row restriction avoids zero-denominator interpretation."
    },
    {
      "check": "Zero-row handling",
      "status": "pass",
      "assessment": "Rows containing zeros are excluded in the stated production domain; positive scaling preserves that eligibility; no all-zero-input success claim."
    },
    {
      "check": "Residual checker",
      "status": "pass",
      "assessment": "Exact rational positive-reference bound; chosen epsilon 1e-12; no ideal-real factor accuracy established."
    },
    {
      "check": "Finite evidence",
      "status": "pass",
      "assessment": "Independently decoded 59 inequalities from binaries: 33 global, 23 sample cross-products, 3 zero-row deletion comparisons."
    },
    {
      "check": "Actual execution boundary",
      "status": "pass",
      "assessment": "Original pinned upstream function assignment with official dependencies; full DESeq2 namespace/S4 execution not tested."
    },
    {
      "check": "Proof and dependencies",
      "status": "pass",
      "assessment": "Pinned Lean 4.32.2 and all nine locked dependencies; selected compilation and module replay passed."
    },
    {
      "check": "Catalog scope",
      "status": "pass",
      "assessment": "Translated-model proof and finite consistency certificates; no R/IEEE-754 refinement or analytic/universal error bound."
    }
  ],
  "check_count": 10,
  "source_sha256": {
    "lake-manifest.json": "36e34686885812ae5099114347f4c49019a347221cc13765e0dbf174a1261d18",
    "CATALOG.md": "7a706498eb0de002ad9cd7cd1e99cd2170c42bb0ef5c7f15f43d6e6d29c22a33",
    "Normalization.lean": "4206ed6b251d3d43e11e9af77496d1bdeb9c32847a2fb8531ef44899658469ee",
    "lakefile.toml": "5ec19a32073e4ee43b4582b22ac9157841add3fe5222c0ac0b3f4a3bd6d7c2a4",
    "CORRESPONDENCE.md": "0792fe6e5cfc7d8eb228e2e6c5ed8b2725434c6a6e8aa81c61f541ddf29b3cc1",
    "ProductionCertificates.lean": "d011ba3a2bcebff4eba612c32178a6189997011421dde44284be1411fe172129",
    "AGENTS.md": "fc030de3bbfa45ec5977554b3242191c754578c8cb53d8ed639d2494f956ffcc",
    "lean-toolchain": "2bdc48adfa58d0017e538a0ad117c5d73d35deec879978f909406a80c8037273"
  },
  "comparison_evidence": {
    "checks": 59,
    "matrices": 10,
    "global_scaling": 33,
    "sample_cross_products": 23,
    "zero_row_deletion": 3,
    "chosen_epsilon": "1/1000000000000",
    "independently_redecoded_max_residual": "1857734846356159/507060240091292604330318224481",
    "max_residual_decimal": 3.663735981392836e-15,
    "global_bitwise_nonidentity_count": 14
  },
  "replay_environment_correction": "First module replay selected host 4.34.1 Init and failed incompatible-header check. Prepending pinned 4.32.2 bin to PATH resolved it; both module replays then passed.",
  "scope_not_rerun": [
    "Full project verification gate and R execution",
    "Full fresh imported-environment replay",
    "R/IEEE-754 refinement"
  ],
  "logical_limit_example": "Replacing the ideal estimator s(K) everywhere by 2*s(K) preserves scaling equivariance, global-scale invariance, normalized ratios, and zero-row deletion identities. These relations therefore do not establish absolute accuracy relative to s(K).",
  "publishable_claim": "Lean proves scaling equivariance for an exact-real translation of DESeq2 1.52.0 default log-median ratio estimator, with positive sample scales and a nonempty all-positive retained set. Separately, 59 recorded-output consistency comparisons across 10 synthetic matrices satisfy a chosen relative tolerance of 1e-12. This is neither an error bound against the ideal estimator nor a refinement proof for R floating-point execution."
}