{
  "runs": [
    {
      "id": "g6-release-1-1-canonical",
      "claim_id": "g6-cross-language-replay",
      "release_id": "G6_RELEASE/1.1",
      "implementations": [
        {
          "name": "Rust",
          "status": "pass",
          "artifact_id": "g6-release-json"
        },
        {
          "name": "Julia",
          "status": "pass",
          "artifact_id": "g6-release-json"
        },
        {
          "name": "pinned TypeScript",
          "status": "pass",
          "artifact_id": "g6-release-json"
        }
      ],
      "expected_output_ref": "/releases/G6_RELEASE_1.1/RELEASE.json",
      "canonical_record_sha256": "92187a21a7ad8ecef384eda3a654aaa49daf46a31422e168eb5871d218c949fa",
      "cubature_frequency_max": 9,
      "scope": "Named frozen reference outputs for the G6_RELEASE/1.1 canonical record. Rust, Julia, and pinned TypeScript. cubature_frequency_max=9. Python and Java are not G₆ canonical-record runtimes.",
      "limitation": "Implementation conformance: the named implementation reproduced the specified reference outputs. This does not establish theorem validity, peer-review status, or independent mathematical reproduction."
    },
    {
      "id": "omega-naught-1-0-jprv",
      "claim_id": "omega-naught-1-0-jprv",
      "release_id": "OMEGA_NAUGHT/1.0",
      "implementations": [
        {
          "name": "Python",
          "status": "pass",
          "artifact_id": "conformance-python"
        },
        {
          "name": "Julia",
          "status": "pass",
          "artifact_id": "conformance-julia"
        },
        {
          "name": "Java",
          "status": "pass",
          "artifact_id": "conformance-java"
        },
        {
          "name": "Rust",
          "status": "pass",
          "artifact_id": "conformance-rust"
        }
      ],
      "expected_output_ref": "/g6/OMEGA_NAUGHT_1_0.txt",
      "canonical_record_sha256": "c3e3146ce37f84a63b73ab6c5a661dcc63f3213f8750d5e71f94b324229d7079",
      "cubature_frequency_max": null,
      "scope": "Named frozen OMEGA_NAUGHT/1.0 manifest outputs. Python, Julia, Java, and Rust. Distinct from the G₆ canonical record.",
      "limitation": "Implementation conformance: the named implementation reproduced the specified reference outputs. This does not establish theorem validity, peer-review status, or independent mathematical reproduction."
    },
    {
      "id": "f22-python-runtime",
      "claim_id": "cubature-f22-degree69",
      "release_id": "CLASS_I_CUBATURE/1.1 corrected release candidate",
      "implementations": [
        {
          "name": "Python 3.12.13 (Omega_Naught_ClassI_f22_exact_verifier.py)",
          "status": "pass",
          "artifact_id": "f22-python-verifier"
        },
        {
          "name": "Julia 1.11.6 (OmegaNaughtClassIF22ExactVerifier.jl)",
          "status": "pass",
          "artifact_id": "f22-julia-verifier"
        }
      ],
      "expected_output_ref": "/cubature/Omega_Naught_ClassI_f22_verification_output.txt",
      "canonical_record_sha256": "c1c2adf668b3a3c4a09ba55a8374fc08d85027b07b911f8126526a9e52f94250",
      "cubature_frequency_max": 22,
      "scope": "Exact finite linear-algebra calculation on fixed X_22. Corrected Python 3.12.13 and Julia 1.11.6 both print CERTIFICATE PASS, minimum orbit (11,11,0), and the unchanged canonical solution digests.",
      "limitation": "This is a two-implementation conformance check of a specified exact finite calculation. It is not peer review, and an implementation derived from the same reference source is not an independent third-party reproduction. External archival fixation remains pending."
    },
    {
      "id": "successor-python-runtime",
      "claim_id": "successor-I15",
      "release_id": "research addendum, not a successor contract",
      "implementations": [
        {
          "name": "Python 3 (Omega_Naught_Successor_Search_Verifier.py)",
          "status": "pass",
          "artifact_id": "successor-python-verifier"
        }
      ],
      "expected_output_ref": "/dynamics/successor_search_certificate.json",
      "canonical_record_sha256": "26d230fba560a5e08f2380207afc5f8b43cdea25ac67de3de1761ab56fc21e5e",
      "cubature_frequency_max": null,
      "scope": "Exact finite-domain successor search. Does not rewrite OMEGA_NAUGHT/1.0 or G6_RELEASE/1.1.",
      "limitation": "Does not accept a successor contract. Serialization, verifier surface, and guarantee-set scoring are not claimed."
    },
    {
      "id": "typed-connection-python-runtime",
      "claim_id": "typed-connection-audit",
      "release_id": "typed-connection-audit/1.0",
      "implementations": [
        {
          "name": "Python 3.10.21 with SymPy 1.14.0 (typed_connection_proof.py)",
          "status": "pass",
          "artifact_id": "typed-connection-py"
        }
      ],
      "expected_output_ref": "/network/typed_connection_proof.runtime.txt",
      "canonical_record_sha256": "1335a532ae210dccae24532e9fccf0ae3c94f5f8ec83d3e81770309ebe6633a6",
      "cubature_frequency_max": null,
      "scope": "De-branded executable audit of typed maps. Exact symbolic identities; Machin/sqrt(5)/pi/lambda enclosures; exhaustive floor equality on D={0,...,32767} with q<lambda; exhaustive 32768×23 remainder reconstruction; seven negative validation paths. Not a joining theorem.",
      "limitation": "Implementation conformance of a named runtime. Not peer review, not independent third-party reproduction, and not a theorem joining Papers I–VII. Radial template identities in the script are algebraic and are not a physical theorem."
    },
    {
      "id": "lean-check-axioms-python-runtime",
      "claim_id": "lean-provenance-formalization",
      "release_id": "omega-provenance/0.1",
      "implementations": [
        {
          "name": "Python 3.10.21 (scripts/check_axioms.py)",
          "status": "pass",
          "artifact_id": "lean-check-axioms"
        }
      ],
      "expected_output_ref": "/formal/check_axioms.runtime.txt",
      "canonical_record_sha256": "f0f843b744e7d04fb8e764c88f021ef93c03a8b85e2f8a1d4d29d2ef8d1868c8",
      "cubature_frequency_max": null,
      "scope": "Theorem-name coverage of evidence/axioms.log against hosted Omega/*.lean. Allowed axioms {propext, Classical.choice, Quot.sound}. Separate from lake build.",
      "limitation": "The checker is not a proof oracle. lake build was run on this archive on 2026-09-13; see lean-lake-build-on-this-archive. Passing this inventory is not peer review, not independent reproduction of Papers I–VII, and not a joining theorem."
    },
    {
      "id": "lean-lake-build-on-this-archive",
      "claim_id": "lean-provenance-formalization",
      "release_id": "omega-provenance/0.1",
      "implementations": [
        {
          "name": "Lean 4.19.0 / Lake 5.0.0-6caaee8 / Mathlib v4.19.0 (lake build; lake env lean Omega/AxiomAudit.lean)",
          "status": "pass",
          "artifact_id": "lean-lake-build-log"
        }
      ],
      "expected_output_ref": "/formal/evidence/current/build.log",
      "canonical_record_sha256": "ddc10580b76d0dd4ec8d9012bf91a78338fc43c003c4f7dbab2421f3c2b760b9",
      "cubature_frequency_max": null,
      "scope": "Kernel-check of hosted omega_provenance v0.1 on this archive, 2026-09-13. 147 theorem reports; axioms {propext, Classical.choice, Quot.sound}. Sources match package SHA256SUMS 28/28.",
      "limitation": "Machine-checking of the selected maps in that package. Not peer review of Papers I–VII, not a joining theorem, not independent third-party reproduction of those papers, and not a cubature certificate."
    },
    {
      "id": "cubature-f2-f21-python-this-archive",
      "claim_id": "cubature-f10-f21",
      "release_id": "OMEGA_NAUGHT_RECOVERED_CUBATURE_EVIDENCE/2026-09-13",
      "implementations": [
        {
          "name": "Python 3.11.2 (verify_classI_f2_f21.r2.py)",
          "status": "pass",
          "artifact_id": "cubature-f2-f21-verifier-r2"
        },
        {
          "name": "Python 3.11.2 (verify_classI_f2_f21.py historical)",
          "status": "pass",
          "artifact_id": "cubature-f2-f21-verifier"
        }
      ],
      "expected_output_ref": "/cubature/evidence/2026-09-13-this-archive/f2_f21.stdout.txt",
      "canonical_record_sha256": "7b3945ad58b76341bbc22e7812a359f64b61a68d413b2668012dc155803edb5e",
      "cubature_frequency_max": 21,
      "scope": "Exact finite identities on recovered classI_exact_certificates_f2_f21.json. Homogeneous harmonic generators. 20 frequencies, 383 identities, 404 positive masses. Distinct from G6_RELEASE/1.1 cubature_frequency_max=9 and from Paper VI.",
      "limitation": "Implementation conformance of recovered source on this archive. Not peer review, not independent third-party reproduction, not an enlargement of Paper VI, and not a maximality claim."
    },
    {
      "id": "cubature-f23-f24-python-this-archive",
      "claim_id": "cubature-f23-f24-existence",
      "release_id": "OMEGA_NAUGHT_RECOVERED_CUBATURE_EVIDENCE/2026-09-13",
      "implementations": [
        {
          "name": "Python 3.11.2 (replay_recovered.py)",
          "status": "pass",
          "artifact_id": "cubature-f23-f24-replay-launcher"
        }
      ],
      "expected_output_ref": "/cubature/evidence/2026-09-13-this-archive/f23_f24.stdout.txt",
      "canonical_record_sha256": "e886510ec03afe014ad143d6d0b45677fc2bb58a7df495374b5780cf79d5b5af",
      "cubature_frequency_max": 24,
      "scope": "Exact finite identities, positivity, and modular rank witnesses on CLASS_I_CUBATURE_F23_F24_EXACT/1.1. 109 identities. python3 -O refused. Distinct from the printed audit extract and from LaTeX-emitted JSON 3ecbf665….",
      "limitation": "Implementation conformance of recovered source on this archive. Not peer review, not independent third-party reproduction, not an enlargement of Paper VI, and not a maximality claim."
    },
    {
      "id": "boundary-reconstruction-r2-this-archive",
      "claim_id": "omega-boundary-reconstruction",
      "release_id": "boundary-reconstruction/2026-09-22.r2",
      "captured_utc": "2026-09-22T12:35:49Z",
      "implementations": [
        {
          "name": "Python 3.10.21 / NumPy 2.2.6 (normal and -O)",
          "status": "pass",
          "artifact_id": "boundary-py"
        }
      ],
      "environment_artifact_id": "boundary-environment",
      "checker_sha256": "ce3e5ea29ca8de60e27e45164903065f340e54826935f88045b0ed715b5e3efe",
      "expected_output_ref": "/geometry/boundary-reconstruction/this_archive_verify.stdout.txt",
      "canonical_record_sha256": "60ad47fa29f0c7ada869555a393e497411f9c8b08344b2850b71c84a840890b1",
      "cubature_frequency_max": null,
      "scope": "Repaired boundary-note checker. Exact rational J-squared spherical moment; numerical NumPy corroboration for the other groups. Both normal and optimized runs pass, and both deliberate error controls are rejected in each mode.",
      "limitation": "Implementation conformance for this identified checker revision. Written proofs remain in the supplementary note and remarks; this run is not an exact certificate for all statements or a proof-assistant run."
    },
    {
      "id": "ten-sample-reconstruction-2026-09-23",
      "claim_id": "omega-ten-sample-reconstruction",
      "release_id": "ten-sample-reconstruction",
      "captured_utc": "2026-09-23T23:53:35Z",
      "implementations": [
        {
          "name": "Python 3.10.21 (normal and -O)",
          "status": "pass",
          "artifact_id": "ten-sample-verifier"
        }
      ],
      "environment_artifact_id": "ten-sample-execution",
      "checker_sha256": "cc850bda469cb33cc9d37c307dceede7e1b4e5ede002957c3ff7497c7a388c0f",
      "expected_output_ref": "/geometry/boundary-reconstruction/ten-sample/verification.txt",
      "canonical_record_sha256": "a6e04971faf30e665f00fc1b60a16488dddce315a83d715291b5298031268be0",
      "cubature_frequency_max": null,
      "scope": "Exact ten-sample checker. Thirteen groups, including 100 cardinal identities and the worked value 721/300. Two rational transport executions support, and do not replace, the written transport argument.",
      "limitation": "Implementation conformance for this checker. The written argument is the hosted Markdown. Not a proof-assistant run, not a new cubature rule, and not an additional source paper."
    },
    {
      "id": "exact-field-interface-2026-09-25",
      "claim_id": "omega-exact-field-interface",
      "release_id": "exact-field-interface",
      "captured_utc": "2026-09-25T02:39:45Z",
      "implementations": [
        {
          "name": "Python 3.10.21 (normal and -O)",
          "status": "pass",
          "artifact_id": "exact-interface-verifier"
        }
      ],
      "environment_artifact_id": "exact-interface-execution",
      "checker_sha256": "d51b7595348d067163c08b88a7726b761662471a1f9b380201114d0112417bfd",
      "expected_output_ref": "/geometry/exact-interface/verification.txt",
      "canonical_record_sha256": "345931205dac7acbf49422ca727e55ea333badc37ce3329f612a6ef7813d3977",
      "cubature_frequency_max": null,
      "scope": "Exact finite checks of the basis sign determinant, the norm identity, the rational reflection, an attained integer disagreement, a continuous infimum that is not a disagreement, one floor identity, the normalized integral of J^2, and the coefficient-record schema.",
      "limitation": "Implementation conformance for this checker. Not a Galois-correspondence proof, not a transcendence proof, not a new cubature rule, and not an additional source paper."
    },
    {
      "id": "floor-kernel-399-2026-09-24",
      "claim_id": "omega-floor-kernel-399",
      "release_id": "floor-kernel-399/2026-09-24",
      "captured_utc": "2026-09-24T00:50:51Z",
      "implementations": [
        {
          "name": "Python 3.10.21 (normal and -O, with and without the site reference)",
          "status": "pass",
          "artifact_id": "floor-kernel-py"
        },
        {
          "name": "Node v22.23.2 (with and without the retrieved bridge)",
          "status": "pass",
          "artifact_id": "floor-kernel-node-verifier"
        }
      ],
      "environment_artifact_id": "floor-kernel-execution",
      "checker_sha256": "dc1b1633628fac20e0cc8fb5f80c37c54d888f496124417b6e71ddbd0b53b8a9",
      "expected_output_ref": "/dynamics/floor-kernel/verification_python.txt",
      "canonical_record_sha256": "3a59103bb189ae68ef0aa4ef9f67525489f3b9243a912b69748a1718ebc1512d",
      "cubature_frequency_max": null,
      "scope": "Unpadded rational-floor kernel on seeds 0 through 32767, the 399 ledger, and one 81-digit round trip. The site-reference stdout matches the supplied transcript.",
      "limitation": "Finite implementation check of the existing map. Not a new theorem, not equality of Q/S with lambda, and not a browser acceptance test. The bare command stdout is recorded separately because it omits the site-comparison line."
    }
  ]
}