{
  "schema_version": "erdos.verification-receipt.v1",
  "release_id": "no5sphere-c8-ge23-alphaevolve-v1",
  "generated_at": "2026-07-10T19:32:33.578426Z",
  "objective": "Given a finite witness and an explicit verification contract, emit a portable receipt or refuse to promote the claim.",
  "classification": {
    "mode": "published_witness_reverification",
    "novelty_claimed": false,
    "optimality_claimed": false,
    "discovered_by_erdos": false,
    "improvement_claimed": false
  },
  "claim": {
    "notation": "C(8) >= 23",
    "scope": "existential_lower_bound",
    "plain_language": "The published 23-point construction contains no five points on one sphere or plane, so at least 23 valid points fit in the 8x8x8 grid.",
    "grid": {
      "dimensions": 3,
      "min": 1,
      "max": 8
    },
    "cardinality": 23,
    "predicate": "every_5_subset_has_nonzero_lifted_5x5_determinant"
  },
  "decision": {
    "status": "accepted",
    "grade": "computed_exact",
    "formal_proof": false,
    "reason": "All 33,649 five-point subsets passed three exact-integer determinant implementations and the persisted Ledger passed strict replay audit."
  },
  "source": {
    "repository": "google-deepmind/alphaevolve_repository_of_problems",
    "commit": "bfd224d0e7763f89eb4a8efe93ac126091f85ed9",
    "path": "experiments/no_5_on_a_sphere/no_5_on_a_sphere.ipynb",
    "symbol": "construction_n_8_8_8",
    "artifact": "source-notebook.ipynb",
    "sha256": "0af65a39d7b5d5d55ba078d19b6dae4b410c66c3395101234a09f0223e5af075"
  },
  "witness": {
    "artifact": "source-witness.json",
    "point_count": 23,
    "unique_count": 23,
    "canonical_sha256": "dcb542187585e5873ecbe0f5cc9c7da6da0224640a0f35b0c2d20eb1028a0d6f",
    "frame_transform": [
      1,
      1,
      1
    ]
  },
  "verification": {
    "status": "pass",
    "arithmetic": "exact_integer",
    "point_count": 23,
    "unique_count": 23,
    "subsets_expected": 33649,
    "subsets_checked": 33649,
    "verifier_disagreements": 0,
    "first_failure": null,
    "witness_sha256": "dcb542187585e5873ecbe0f5cc9c7da6da0224640a0f35b0c2d20eb1028a0d6f",
    "verifiers": [
      {
        "id": "bareiss",
        "implementation": "no5sphere_problem.det5",
        "status": "pass"
      },
      {
        "id": "cofactor",
        "implementation": "adversary_verify.det_cofactor",
        "status": "pass"
      },
      {
        "id": "permutation_sum",
        "implementation": "adversary_verify.det_permsum",
        "status": "pass"
      }
    ]
  },
  "provenance": {
    "run_id": "01KX6R8RWCT1GYANHA953YFRW6",
    "code_commit": "2622663c1f08d4190af18cd9ac299ad41c949372",
    "clean_tree_at_start": true,
    "ledger_sqlite": {
      "path": "run.sqlite",
      "sha256": "7775933fc9d12b5d31bc19567b23965303940739fd7c4781e226b3ebe479ce01"
    },
    "ledger_export": {
      "path": "ledger.json",
      "sha256": "32ed8448da0adeb73e38912cbb5ac7dc0090548d1e89b5361294be4b07a73c07"
    },
    "replay_audit": {
      "path": "replay.json",
      "sha256": "884eac350bef9b41480521d757a4ed5342074d8a2b2bd746f12495f46dfa7734"
    },
    "replay_status": "consistent",
    "independent_witness_rechecks": 1,
    "code_sha256": {
      "release_contract.py": "78e1938162b57f7c1ee4a9e5cc368d8da0fde43afb565f8c09472d6a4e8836d4",
      "no5sphere_problem.py": "502b342f5795426eae565ca34fa0a61b843c32d83dfb955c2e87e6993265a0f5",
      "adversary_verify.py": "9ba7f463ac32dc26d7c7572db263cb0b3b0b95f464cba332cb455f1cbdb3b6d4",
      "ledger.py": "7190b09ed29f4603524db4281225e9f67120c838ad485a08d6cafd1c0656bd8f",
      "replay.py": "6ffcbee01e2aaadeb842b1c75837abb6958f5ae638ed95e4f97e57ff80018716",
      "verify_release.py": "35f79e08d574d4cec42acf4042ea90a3cd1ddb3218565a9639109de1bd029663"
    }
  },
  "integrity": {
    "stable_result_sha256": "e99ef00f5a2684895a19ec5bb66a39361d4b203cbcc5d1a07331d0876be95f79"
  },
  "limits": [
    "This re-verifies a published construction; Erdős did not discover it.",
    "The receipt establishes only the lower bound C(8) >= 23, not optimality or equality.",
    "The evidence grade is exact computation, not a Lean formal proof.",
    "The current public release contract covers this supported finite witness, not arbitrary mathematics."
  ],
  "reproduce": {
    "verify_bundle": "python verify_release.py receipt.json --strict",
    "rebuild_from_repo": "python release.py build no5sphere-c8-ge23 --out <directory>"
  }
}