{
  "reviewed_commit": "72ba2a58fdb24eaac5e2bda86b8c2a05a66cf291",
  "owner_unchanged": true,
  "result": "No mathematical theorem defect or catalog-blocking scope error found. Suitable for verified-output-checker classification with stated boundaries.",
  "checks": [
    {
      "check": "Accepted input/output relation",
      "status": "pass",
      "assessment": "Acceptance implies valid decoded input and structural equality to expected output."
    },
    {
      "check": "Groups and masks",
      "status": "pass",
      "assessment": "Exact active-category order, missing assignments excluded, masked-only groups retained."
    },
    {
      "check": "Feature identity",
      "status": "pass",
      "assessment": "Exact feature list/order and corresponding sum positions."
    },
    {
      "check": "Source identity",
      "status": "pass",
      "assessment": "Source index/name list equals selected serialized input identities; adapter-supplied witness, no execution trace."
    },
    {
      "check": "Natural-number arithmetic",
      "status": "pass",
      "assessment": "Unbounded Nat sums; valid dimensions rule out default-zero ambiguity for included feature positions."
    },
    {
      "check": "Sum bounds",
      "status": "pass",
      "assessment": "Every source entry and selected group/feature sum at most 2^53."
    },
    {
      "check": "Modular model",
      "status": "pass",
      "assessment": "Bounded prefix and mod-2^64 models exact; no upstream machine-code or IEEE-754 refinement."
    },
    {
      "check": "Decoding boundary",
      "status": "pass",
      "assessment": "Observed finite binary64 values decoded as exact integers via trusted Python; no tolerance-based acceptance."
    },
    {
      "check": "Mathematical verification",
      "status": "pass",
      "assessment": "General and Observed compiled and module-replayed; 41 positive and 14 negative concrete certificates."
    },
    {
      "check": "Catalog scope",
      "status": "pass",
      "assessment": "Truthful verified-output-checker classification; synthetic execution evidence; no whole-package or scientific guarantee."
    }
  ],
  "check_count": 10,
  "proof_source_sha256": "6370f25f8e4eee9e2aa1c859582c1b944658c2a605e22a5edfa4976523843a81",
  "observed_source_sha256": "0070878c71b7b1baf8fa3630d03b0d37c83527c7aa3f4000b289c30f45742968",
  "general_audited_declarations": 9,
  "observed_audited_declarations": 55,
  "verification": {
    "module_compilation": "passed",
    "module_replay": "passed",
    "fresh_imported_environment_replay": "not run; installed pinned Std dependencies reused",
    "Scanpy_runtime_reexecution": "not run; recorded transcripts and serializer/call path inspected"
  },
  "recorded_cases": {
    "accepted": 41,
    "rejected": 14,
    "dense": 13,
    "csr": 14,
    "csc": 14,
    "largest_matrix_shape": [
      7,
      3
    ],
    "dense_binary64_cells_independently_checked": 58
  },
  "publishable_claim": "For the stated bounded nonnegative-count domain, a Lean-proved checker certifies that decoded Scanpy grouped-sum outputs equal the specified sums of the serialized input, preserving group and feature labels and validating adapter-supplied source-membership witnesses. Certificates cover 41 recorded synthetic runs of pinned Scanpy across dense, CSR and CSC backends.",
  "retained_boundaries": [
    "Faithful input/output extraction, binary64 decoding and serialization are trusted.",
    "Source witnesses identify specified contributing rows, not internally observed execution provenance.",
    "Arithmetic bounds concern a mathematical reduction model; original Scanpy/Numba/SciPy and IEEE-754 semantics are not refined.",
    "Printable/nonempty labels, nonempty dimensions and canonical sparse storage include adapter-side conditions, not all Lean valid checks.",
    "Finite synthetic runs do not establish universal upstream correctness, scale performance or scientific validity."
  ]
}