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      "title": "Python exact verifier for frequency 22",
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      "title": "Python exact verifier for frequency 22, revision r2",
      "filename": "Omega_Naught_ClassI_f22_exact_verifier.r2.py",
      "path": "/cubature/Omega_Naught_ClassI_f22_exact_verifier.r2.py",
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      "runtime_note": "Documented revision of the original certificate verifier. Adds a __debug__ guard that refuses python3 -O / -OO / PYTHONOPTIMIZE. Does not change the certificate, theorem, or canonical solution digests. Original 16972-byte verifier remains the zip and SHA256SUMS member.",
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      "id": "f22-julia-verifier",
      "title": "Julia exact verifier for frequency 22",
      "filename": "OmegaNaughtClassIF22ExactVerifier.jl",
      "path": "/cubature/OmegaNaughtClassIF22ExactVerifier.jl",
      "language": "Julia",
      "runtime_note": "Stdlib SHA and Printf. Official Julia 1.11.6 prints CERTIFICATE PASS with unchanged canonical solution digests.",
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      "title": "Julia f=22 runtime record",
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      "title": "Frequency-22 certificate package (single archive)",
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      "path": "/cubature/Omega_Naught_ClassI_f22_certificate_package.zip",
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      "runtime_note": "Python and Julia verifiers, both PASS transcripts, README, licenses, RELEASE.json, checksums, and certificate directory. ZIP is a transport convenience; independent compressors need not match these bytes.",
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      "title": "Python verification transcript",
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      "title": "Degree-69 canonical 52-orbit solution",
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      "path": "/cubature/certificates/f22_degree69_solution.canonical.txt",
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      "title": "Degree-70/71 canonical 52-orbit solution",
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      "path": "/cubature/certificates/f22_degree71_solution.canonical.txt",
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      "path": "/cubature/certificates/f22_degree69_orbit_masses.csv",
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      "runtime_note": "Exact Q(sqrt(5)) components for all 52 degree-69 orbit masses.",
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      "title": "Degree-70/71 orbit masses CSV",
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      "path": "/cubature/certificates/f22_degree71_orbit_masses.csv",
      "language": "CSV",
      "runtime_note": "Exact Q(sqrt(5)) components for all 52 forced degree-70/71 orbit masses, including the negative orbit (21,1,0).",
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    {
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      "title": "Exact dual/Farkas coefficient vector",
      "filename": "f22_dual_coefficients.canonical.txt",
      "path": "/cubature/certificates/f22_dual_coefficients.canonical.txt",
      "language": "canonical text",
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    {
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      "filename": "f22_moment_system_spec.json",
      "path": "/cubature/certificates/f22_moment_system_spec.json",
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      "runtime_note": "Orbit representatives, invariant pairs, free columns, and published solution digests.",
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    {
      "id": "f22-negative-orbit",
      "title": "Exact negative mass at orbit (21,1,0)",
      "filename": "f22_negative_orbit.json",
      "path": "/cubature/certificates/f22_negative_orbit.json",
      "language": "JSON",
      "runtime_note": "Exact Q(sqrt(5)) negative mass and matching dual spherical mean. Decimal orientation is not the certificate.",
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    {
      "id": "f22-cert-sha256sums",
      "title": "SHA-256 manifest for f=22 certificate files",
      "filename": "SHA256SUMS.txt",
      "path": "/cubature/certificates/SHA256SUMS.txt",
      "language": "text",
      "runtime_note": "SHA-256 and filenames for the finite certificate dump directory.",
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      "title": "Frequency-22 research addendum v1.1 (corrected)",
      "filename": "Omega_Naught_ClassI_f22_Research_Addendum_v1.1.pdf",
      "path": "/docs/Omega_Naught_ClassI_f22_Research_Addendum_v1.1.pdf",
      "language": "PDF",
      "runtime_note": "Corrected 27 August 2026. Minimum positive orbit (11,11,0). Python 3.12.13 and Julia 1.11.6 CERTIFICATE PASS. Canonical solution digests unchanged. Not part of G6_RELEASE/1.1.",
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      "title": "Frequency-22 research addendum v1.0 (superseded)",
      "filename": "Omega_Naught_ClassI_f22_Research_Addendum_v1.0_superseded.pdf",
      "path": "/docs/Omega_Naught_ClassI_f22_Research_Addendum_v1.0_superseded.pdf",
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      "runtime_note": "SUPERSEDED. Incorrectly named minimum orbit (22,0,0) after binary64 comparison and listed only Python reproduction. Theorem and canonical solution digests remain valid. Replaced by v1.1.",
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      "title": "Cubature public-boundary correction package",
      "filename": "Omega_Naught_G6_Cubature_f22_All_In_One_Site_Update.pdf",
      "path": "/docs/Omega_Naught_G6_Cubature_f22_All_In_One_Site_Update.pdf",
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      "runtime_note": "Correction package for the public cubature boundary.",
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    {
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      "title": "CLASS_I_CUBATURE/1.1 corrected release candidate",
      "filename": "CLASS_I_CUBATURE_1_1.json",
      "path": "/cubature/CLASS_I_CUBATURE_1_1.json",
      "language": "JSON",
      "runtime_note": "Corrected release candidate pending external archival fixation. Inclusive frequency intervals; three correction causes. Does not rewrite CLASS_I_CUBATURE/1.0 or G6_RELEASE/1.1. Frequency 22 minimum orbit (11,11,0). Recovered 10–21 and 23–24 exact packages are now hosted; they do not enlarge Paper VI.",
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    {
      "id": "cubature-f23-f24-theorem",
      "title": "Positive H₃-invariant cubature on X₂₃ and X₂₄",
      "filename": "X23_X24_positive_existence.md",
      "path": "/cubature/X23_X24_positive_existence.md",
      "language": "Markdown",
      "runtime_note": "Locally hosted existence theorem, 3 September 2026. Proof text. Companion 5 September 2026 dossier adds printed finite-audit data. The 117 exact Q(sqrt(5)) masses, runnable verifier, and 109-residual ledger are now hosted as separate artifacts under /cubature/. Printed audit extract remains a distinct file. Does not enlarge Paper VI. Frozen G6 bytes unchanged.",
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    {
      "id": "cubature-f23-f24-audit-extract",
      "title": "Printed f=23,24 finite-audit extract from the typed-network dossier",
      "filename": "ClassI_Cubature_f23_f24_audit_extract_v1.1.json",
      "path": "/cubature/ClassI_Cubature_f23_f24_audit_extract_v1.1.json",
      "language": "JSON",
      "runtime_note": "Extract of tables, hashes, free orbits, minima, and the quoted 5 September 2026 same-environment replay. Not the canonical one-line certificate (e886510e…) and not a runnable verifier. Keep this extract distinct from the hosted full certificate.",
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      "title": "Typed network exact proof dossier v1.0",
      "filename": "OMEGA_NAUGHT_Typed_Network_Exact_Proof_Dossier_v1.0.pdf",
      "path": "/docs/OMEGA_NAUGHT_Typed_Network_Exact_Proof_Dossier_v1.0.pdf",
      "language": "PDF",
      "runtime_note": "Locally hosted 5 September 2026 proof dossier. Network audit v1.0; cubature certificate cited as v1.1. Not a joining theorem. LaTeX filecontents of the 117 masses and runnable verifier are not extractable from this PDF; those originals are now hosted separately under /cubature/. Frozen G6 bytes unchanged.",
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    },
    {
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      "title": "Corrected f=22 release manifest",
      "filename": "RELEASE.json",
      "path": "/cubature/RELEASE.json",
      "language": "JSON",
      "runtime_note": "16-payload inventory plus licenses. Inventory digest 23c1d9e8…. ZIP excluded from the canonical inventory. Status candidate_pending_external_fixation.",
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      "title": "Pin file for the corrected f=22 release manifest",
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      "path": "/cubature/RELEASE.sha256",
      "language": "text",
      "runtime_note": "SHA-256 of RELEASE.json.",
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      "id": "f22-sha256sums",
      "title": "Top-level SHA-256 manifest for the corrected f=22 package",
      "filename": "SHA256SUMS.txt",
      "path": "/cubature/SHA256SUMS.txt",
      "language": "text",
      "runtime_note": "sha256sum format over the 16 listed files.",
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      "title": "CLASS_I_CUBATURE/1.0 frozen contract",
      "filename": "CLASS_I_CUBATURE_1_0.json",
      "path": "/g6/CLASS_I_CUBATURE_1_0.json",
      "language": "JSON",
      "runtime_note": "Frozen. Scope 1 ≤ f ≤ 9.",
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      "id": "orbit-csv",
      "title": "Orbit masses f=1…9",
      "filename": "orbit_masses_f1_f9.csv",
      "path": "/g6/data/orbit_masses_f1_f9.csv",
      "language": "CSV",
      "runtime_note": "Frozen exact weights for Paper VI frequencies.",
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    {
      "id": "f9-csv",
      "title": "Frequency-9 affine family",
      "filename": "f9_affine_family.csv",
      "path": "/g6/data/f9_affine_family.csv",
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      "runtime_note": "Frozen f=9 positivity interval members.",
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      "path": "/papers/Exact_Positive_Icosahedral_Cubature_Integrated_Preprint_v1.3.pdf",
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      "title": "Paper VII local PDF v1.6",
      "filename": "OMEGA_Paper_VII_v1.6.0.pdf",
      "path": "/papers/OMEGA_Paper_VII_v1.6.0.pdf",
      "language": "PDF",
      "runtime_note": "Local mirror of the Paper VII Zenodo preprint v1.6. Authoritative identifier is DOI 10.5281/zenodo.22233573. Companion generator is not a theorem checker.",
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      "title": "Paper VII local PDF v1.4 (superseded)",
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      "path": "/papers/OMEGA_Paper_VII_v1.4.pdf",
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      "path": "/geometry/kernel/omega_reference_geometry.py",
      "language": "Python 3",
      "runtime_note": "Exports canonical landmarks as JSON and a sampled OBJ polyline. Landmark coordinates are direct evaluations of the closed formulas. Generator defaults write JSON/OBJ into the current working directory. The unchanged verifier reads generated/JSON and generated/OBJ. Not a theorem checker.",
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      "title": "Paper VII unit-scale landmark record",
      "filename": "OMEGA_local_kernel_v1_6_0.json",
      "path": "/geometry/kernel/OMEGA_local_kernel_v1_6_0.json",
      "language": "JSON",
      "runtime_note": "Canonical unit-scale landmarks, signed bearings, Gram factorization fields, and complete center-angle matrix. Schema OMEGA_MARKED_REFERENCE_GEOMETRY/1.2. Direct evaluation of the v1.6 formulas.",
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      "claim_ids": [
        "lean-provenance-formalization"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "lean-setup-log",
      "title": "Author lake-update transcript",
      "filename": "setup_lake_update.log",
      "path": "/formal/evidence/setup_lake_update.log",
      "language": "text",
      "runtime_note": "Author-supplied lake update log. Includes a ProofWidgets cloud-release fetch failure in that session. Not generated on this archive.",
      "bytes": 1722,
      "sha256": "62555658e57af67df06d8ddb4fc1507ed6b8e6f43f63a289aefd1ee4f7e70768",
      "claim_ids": [
        "lean-provenance-formalization"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "lean-check-axioms-runtime",
      "title": "Named Python axiom-coverage runtime",
      "filename": "check_axioms.runtime.txt",
      "path": "/formal/check_axioms.runtime.txt",
      "language": "text",
      "runtime_note": "Python 3.10.21 PASS: 147 theorem reports; axioms Classical.choice, Quot.sound, propext. Inventory of the author axiom log against hosted sources. Not lake build and not a proof oracle.",
      "bytes": 926,
      "sha256": "f0f843b744e7d04fb8e764c88f021ef93c03a8b85e2f8a1d4d29d2ef8d1868c8",
      "claim_ids": [
        "lean-provenance-formalization"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "lean-docx-transcription",
      "title": "Word transcription of the v0.1 ZIP",
      "filename": "LEAN_Proof_Complete_Final.docx",
      "path": "/formal/LEAN_Proof_Complete_Final.docx",
      "language": "DOCX",
      "runtime_note": "Word transcription from which the 29 package files were recovered. Hosted sources match SHA256SUMS. The original ZIP is not hosted; stated ZIP SHA-256 is f77f83d0edd127b5377f7c796963ec9d0cb5610bae14116361b9c6aec8437178.",
      "bytes": 75151,
      "sha256": "275da4ea14130d21aa1b797b643ec78192e195780bfd8352bac699a75b73542e",
      "claim_ids": [
        "lean-provenance-formalization"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "lean-lake-build-log",
      "title": "lake build transcript generated on this archive",
      "filename": "build.log",
      "path": "/formal/evidence/current/build.log",
      "language": "text",
      "runtime_note": "2026-09-13 lake build of hosted omega_provenance v0.1. Lean 4.19.0 commit 6caaee842e94, Lake 5.0.0-6caaee8. Modules Built, not Replayed. Ends with Build completed successfully. Distinct from the author evidence/build.log. Toolchain and .lake are not hosted.",
      "bytes": 1960,
      "sha256": "ddc10580b76d0dd4ec8d9012bf91a78338fc43c003c4f7dbab2421f3c2b760b9",
      "claim_ids": [
        "lean-provenance-formalization"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "lean-lake-axioms-log",
      "title": "lake axiom-audit transcript generated on this archive",
      "filename": "axioms.log",
      "path": "/formal/evidence/current/axioms.log",
      "language": "text",
      "runtime_note": "2026-09-13 lake env lean Omega/AxiomAudit.lean. 147 theorem reports; axioms {propext, Classical.choice, Quot.sound}. Byte-identical to the author evidence/axioms.log.",
      "bytes": 11804,
      "sha256": "82dae0644b5ce591c3e4af7bf9fdbfa6aeec11591560cb785ab0727a65d8eda1",
      "claim_ids": [
        "lean-provenance-formalization"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "lean-lake-environment",
      "title": "Lean lake-run environment record",
      "filename": "ENVIRONMENT.json",
      "path": "/formal/evidence/current/ENVIRONMENT.json",
      "language": "JSON",
      "runtime_note": "Machine record of the 2026-09-13 lake build: versions, commands, axiom list, 147 theorem names, transcript hashes. Schema OMEGA_NAUGHT_LEAN_RUN/1.0. Not a joining theorem and not independent reproduction of Papers I–VII.",
      "bytes": 9793,
      "sha256": "622ce56958f1dce7e28a26615c618313dc7d62046932301cdac06880ba7000ff",
      "claim_ids": [
        "lean-provenance-formalization"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "lean-sorry-scan",
      "title": "sorry / admit / native_decide scan of hosted Lean sources",
      "filename": "sorry_scan.txt",
      "path": "/formal/evidence/current/sorry_scan.txt",
      "language": "text",
      "runtime_note": "Python identifier scan of hosted Omega.lean and Omega/*.lean on 2026-09-13. Zero sorry, admit, or native_decide hits in 14 files.",
      "bytes": 1610,
      "sha256": "58b5ac839405753ff6df9434f716cf12b9f4f9d61f59f8e7333fa2577523ed69",
      "claim_ids": [
        "lean-provenance-formalization"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "lean-lake-check-axioms-runtime",
      "title": "Named Python axiom-coverage runtime of the current axiom log",
      "filename": "check_axioms.runtime.txt",
      "path": "/formal/evidence/current/check_axioms.runtime.txt",
      "language": "text",
      "runtime_note": "Python 3.10.21 PASS on evidence/current/axioms.log: 147 theorem reports; axioms Classical.choice, Quot.sound, propext. Inventory of the 2026-09-13 lake axiom audit. Not a proof oracle.",
      "bytes": 1226,
      "sha256": "e10e6ea8c8bdd6c78a82a5b734359126e96e8e60106425f418943b6ba25af884",
      "claim_ids": [
        "lean-provenance-formalization"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "lean-lake-current-sha256sums",
      "title": "SHA-256 inventory of the current Lean run transcripts",
      "filename": "SHA256SUMS",
      "path": "/formal/evidence/current/SHA256SUMS",
      "language": "text",
      "runtime_note": "Digests of the five current-run files. Distinct from the author package SHA256SUMS, which is unchanged (28/28).",
      "bytes": 408,
      "sha256": "c6eb2c9233b8da93d9d91f541c5b2f35d0a567bd360d091d4e4f8828fff01bae",
      "claim_ids": [
        "lean-provenance-formalization"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-docx",
      "title": "Julia proof companion Word transcription",
      "filename": "OMEGA_NAUGHT_Julia_Proof_v0.1_Complete_Verbatim.docx",
      "path": "/julia-proofs/downloads/OMEGA_NAUGHT_Julia_Proof_v0.1_Complete_Verbatim.docx",
      "language": "Word",
      "runtime_note": "718-page verbatim transcription used to recover the 68 original members. SHA-256 of this file is of the hosted Word bytes. Not a source paper.",
      "bytes": 1795998,
      "sha256": "7df27d9efd8bc5cfab1129b598c59bf0f0f47d12b5a1f581751c3fee41616bc7",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reconstructed-zip",
      "title": "Julia proof companion reconstructed transport ZIP",
      "filename": "OMEGA_NAUGHT_Julia_Proof_v0.1.reconstructed-from-members.zip",
      "path": "/julia-proofs/downloads/OMEGA_NAUGHT_Julia_Proof_v0.1.reconstructed-from-members.zip",
      "language": "ZIP",
      "runtime_note": "Transport ZIP rebuilt from recovered members with a fixed 2026-09-12 timestamp and DEFLATE. Independent compressors need not match these bytes. This is not the author-stated original ZIP. Author-stated original ZIP SHA-256 ef8f1eb75b83f1e5763d280374eb8b73d9ab00b8dcb76b1824aee771869cd27a was not recovered as those exact container bytes.",
      "bytes": 1683196,
      "sha256": "b5d4e46ac32ac4ec08f96a6fc609fe8c8c3a291b7226809c2e79c3adac2e26ab",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-inventory",
      "title": "Julia proof companion hosted inventory",
      "filename": "INVENTORY.json",
      "path": "/julia-proofs/downloads/INVENTORY.json",
      "language": "JSON",
      "runtime_note": "Index of the 68 recovered members with SHA-256. Extra hosting file; not one of the original 68.",
      "bytes": 15157,
      "sha256": "3dbce6bed7dcac0e3051c305391436af883422dbea2a7c41fdccba84b8efcb5b",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-dependencies-md",
      "title": "Typed mathematical dependency guide",
      "filename": "DEPENDENCIES.md",
      "path": "/julia-proofs/DEPENDENCIES.md",
      "language": "Markdown",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 5898,
      "sha256": "3a4502b215f486d4c2dd718cfec247befe424a47ce354a21ccb3168953cb40d1",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-proofs-md",
      "title": "Julia proof chapters P01–P13",
      "filename": "PROOFS.md",
      "path": "/julia-proofs/PROOFS.md",
      "language": "Markdown",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 26771,
      "sha256": "a1da438398d4df276d5abd441c8baa654ff98312ece80e9211a6db05a40cd048",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-project-toml",
      "title": "OmegaNaughtProofs 0.1.0 project file",
      "filename": "Project.toml",
      "path": "/julia-proofs/Project.toml",
      "language": "TOML",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 262,
      "sha256": "0b350943d4b1fd4532f02177de414f7406be8fb75372d10cf3e8677d85c77211",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-readme-md",
      "title": "Julia proof companion README",
      "filename": "README.md",
      "path": "/julia-proofs/README.md",
      "language": "Markdown",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 6289,
      "sha256": "71de22038e8c4ebe9bb391d7e4b995adf4061b1494e4d075f629c73bd0746c78",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reproduction-md",
      "title": "Author Julia 1.11.6 reproduction record",
      "filename": "REPRODUCTION.md",
      "path": "/julia-proofs/REPRODUCTION.md",
      "language": "Markdown",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 8273,
      "sha256": "2659313e6df58b03e6a1181fd786015d02e0091ef300110cf78685a8f9a0195b",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-sha256sums",
      "title": "Julia proof companion SHA256SUMS",
      "filename": "SHA256SUMS",
      "path": "/julia-proofs/SHA256SUMS",
      "language": "text",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 6301,
      "sha256": "716a6659ff5893f722854e13a6a97e7d30235e7f5268ad3a4e02c21cd25096f9",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-theorems-toml",
      "title": "147 theorem inventory",
      "filename": "THEOREMS.toml",
      "path": "/julia-proofs/THEOREMS.toml",
      "language": "TOML",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 89430,
      "sha256": "8b27cf29d5c9c738fa00eea721168ca7409ad2ce97417123e5263fdb7abc4c35",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-theorem_guide-md",
      "title": "147 theorem guide",
      "filename": "THEOREM_GUIDE.md",
      "path": "/julia-proofs/THEOREM_GUIDE.md",
      "language": "Markdown",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 89735,
      "sha256": "7a609115531637ecd1ef04b2b125e2f5e795875fad20b4dab1cd45ee6d966c70",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-translation-md",
      "title": "Julia/Lean translation conventions",
      "filename": "TRANSLATION.md",
      "path": "/julia-proofs/TRANSLATION.md",
      "language": "Markdown",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 9240,
      "sha256": "9b6c232e062806665a3223f90edad4e838988f188b36bfb95a147d39245eadb7",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o0-gap_blocks-csv",
      "title": "Julia proof companion evidence/O0/gap_blocks.csv",
      "filename": "gap_blocks.csv",
      "path": "/julia-proofs/evidence/O0/gap_blocks.csv",
      "language": "CSV",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 4383,
      "sha256": "eb5fdeaf1aeef4d3fa13f880fcbd19300974093bad98beb2bf3f84e7cafc033f",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o0-polynomial_certificates-tsv",
      "title": "Julia proof companion evidence/O0/polynomial_certificates.tsv",
      "filename": "polynomial_certificates.tsv",
      "path": "/julia-proofs/evidence/O0/polynomial_certificates.tsv",
      "language": "TSV",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 8055,
      "sha256": "63d3c849d626e3b808f35d376969f084c273ea61774f5538b9163006fbdea8f2",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o0-precision_sweep-csv",
      "title": "Julia proof companion evidence/O0/precision_sweep.csv",
      "filename": "precision_sweep.csv",
      "path": "/julia-proofs/evidence/O0/precision_sweep.csv",
      "language": "CSV",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 559,
      "sha256": "7e2c0313ff402b628cdd1ad809dc9539a4e594af2be556aa77353756cf59b5e3",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o0-rational_enclosures-tsv",
      "title": "Julia proof companion evidence/O0/rational_enclosures.tsv",
      "filename": "rational_enclosures.tsv",
      "path": "/julia-proofs/evidence/O0/rational_enclosures.tsv",
      "language": "TSV",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 40480,
      "sha256": "7fd085ae638ef4ff8a3e0486d371d30ee4897bc4dc737584e54a9c7c1895d64b",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o0-results-toml",
      "title": "Julia proof companion evidence/O0/results.toml",
      "filename": "results.toml",
      "path": "/julia-proofs/evidence/O0/results.toml",
      "language": "TOML",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 1703,
      "sha256": "28fc2001eaa7d9591b769f37d097f145c60dd37442241060d24fae5a9ae5aa20",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o0-state_certificate-csv",
      "title": "O0 complete state certificate",
      "filename": "state_certificate.csv",
      "path": "/julia-proofs/evidence/O0/state_certificate.csv",
      "language": "CSV",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 1656880,
      "sha256": "b4269d3a331b2f2da0b4d55e9b012fde64a7f8e7b02a947d5e90cf607ccde466",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o0-log",
      "title": "Author O0 execution log",
      "filename": "O0.log",
      "path": "/julia-proofs/evidence/O0.log",
      "language": "text",
      "runtime_note": "Author-supplied Julia 1.11.6 transcript. Not generated on this archive. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 1552,
      "sha256": "93db690c00cc4ef19270895bd5a78fd497b67a27c58f871692d03575d3564df4",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o3-gap_blocks-csv",
      "title": "Julia proof companion evidence/O3/gap_blocks.csv",
      "filename": "gap_blocks.csv",
      "path": "/julia-proofs/evidence/O3/gap_blocks.csv",
      "language": "CSV",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 4383,
      "sha256": "eb5fdeaf1aeef4d3fa13f880fcbd19300974093bad98beb2bf3f84e7cafc033f",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o3-polynomial_certificates-tsv",
      "title": "Julia proof companion evidence/O3/polynomial_certificates.tsv",
      "filename": "polynomial_certificates.tsv",
      "path": "/julia-proofs/evidence/O3/polynomial_certificates.tsv",
      "language": "TSV",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 8055,
      "sha256": "63d3c849d626e3b808f35d376969f084c273ea61774f5538b9163006fbdea8f2",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o3-precision_sweep-csv",
      "title": "Julia proof companion evidence/O3/precision_sweep.csv",
      "filename": "precision_sweep.csv",
      "path": "/julia-proofs/evidence/O3/precision_sweep.csv",
      "language": "CSV",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 559,
      "sha256": "7e2c0313ff402b628cdd1ad809dc9539a4e594af2be556aa77353756cf59b5e3",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o3-rational_enclosures-tsv",
      "title": "Julia proof companion evidence/O3/rational_enclosures.tsv",
      "filename": "rational_enclosures.tsv",
      "path": "/julia-proofs/evidence/O3/rational_enclosures.tsv",
      "language": "TSV",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 40480,
      "sha256": "7fd085ae638ef4ff8a3e0486d371d30ee4897bc4dc737584e54a9c7c1895d64b",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o3-results-toml",
      "title": "Julia proof companion evidence/O3/results.toml",
      "filename": "results.toml",
      "path": "/julia-proofs/evidence/O3/results.toml",
      "language": "TOML",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 1703,
      "sha256": "28fc2001eaa7d9591b769f37d097f145c60dd37442241060d24fae5a9ae5aa20",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o3-state_certificate-csv",
      "title": "O3 complete state certificate",
      "filename": "state_certificate.csv",
      "path": "/julia-proofs/evidence/O3/state_certificate.csv",
      "language": "CSV",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 1656880,
      "sha256": "b4269d3a331b2f2da0b4d55e9b012fde64a7f8e7b02a947d5e90cf607ccde466",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-o3-log",
      "title": "Author O3 execution log",
      "filename": "O3.log",
      "path": "/julia-proofs/evidence/O3.log",
      "language": "text",
      "runtime_note": "Author-supplied Julia 1.11.6 transcript. Not generated on this archive. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 1552,
      "sha256": "93db690c00cc4ef19270895bd5a78fd497b67a27c58f871692d03575d3564df4",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-optimization_comparison-tsv",
      "title": "O0/O3 certificate identity table",
      "filename": "optimization_comparison.tsv",
      "path": "/julia-proofs/evidence/optimization_comparison.tsv",
      "language": "TSV",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 973,
      "sha256": "6ba9b6c2f381fb21bbc907bed68eeb597ebfecd84ed38815ef1ef7ff3ac34457",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-run_manifest-toml",
      "title": "Author run manifest",
      "filename": "run_manifest.toml",
      "path": "/julia-proofs/evidence/run_manifest.toml",
      "language": "TOML",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 1164,
      "sha256": "ee7e51cbfb88cd8c18713119d9a1e083ef2d3bfb3afa40f5d2774944f15f1138",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-evidence-source_and_environment-json",
      "title": "Julia proof companion evidence/source_and_environment.json",
      "filename": "source_and_environment.json",
      "path": "/julia-proofs/evidence/source_and_environment.json",
      "language": "JSON",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 406,
      "sha256": "3bcdc38005d5953dd77b10ab299a78c983b09a41230b7f779bc2b0a29ffa5e8d",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-examples-reconstruction-jl",
      "title": "Exact reconstruction example",
      "filename": "reconstruction.jl",
      "path": "/julia-proofs/examples/reconstruction.jl",
      "language": "Julia",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 1201,
      "sha256": "045d1f82645dd14fa2bdc114288cefdad44c922c06d76d61f299469f1a7ae139",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-julia-version",
      "title": "Julia proof companion julia-version",
      "filename": "julia-version",
      "path": "/julia-proofs/julia-version",
      "language": "text",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 7,
      "sha256": "0ee46b684ed08be98c69d1631b632b5a5607c638cd1b8cce2e4bdb9443b7d0b3",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-affine-lean",
      "title": "Julia proof companion reference/Lean/Omega/Affine.lean",
      "filename": "Affine.lean",
      "path": "/julia-proofs/reference/Lean/Omega/Affine.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 2460,
      "sha256": "bf8c5e04ee15ad4b1ec14cae878fdaf572d374e635f31191d750ab0c90de0121",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-axiomaudit-lean",
      "title": "Julia proof companion reference/Lean/Omega/AxiomAudit.lean",
      "filename": "AxiomAudit.lean",
      "path": "/julia-proofs/reference/Lean/Omega/AxiomAudit.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 5645,
      "sha256": "4a0bdc5680cfb7123d6a0a206bb96bdedd6c3c5a49cc15a3d6835efe302efe07",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-constants-lean",
      "title": "Julia proof companion reference/Lean/Omega/Constants.lean",
      "filename": "Constants.lean",
      "path": "/julia-proofs/reference/Lean/Omega/Constants.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 2693,
      "sha256": "a622442855d7d565b8a2ddf9364980f4919638c456229be4f2f4887a3eeea3fa",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-dimension-lean",
      "title": "Julia proof companion reference/Lean/Omega/Dimension.lean",
      "filename": "Dimension.lean",
      "path": "/julia-proofs/reference/Lean/Omega/Dimension.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 4963,
      "sha256": "8f44a603b1448576055ffba4edaf62ca6a83773767962792fe785ea53f24b32f",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-extinction-lean",
      "title": "Julia proof companion reference/Lean/Omega/Extinction.lean",
      "filename": "Extinction.lean",
      "path": "/julia-proofs/reference/Lean/Omega/Extinction.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 1399,
      "sha256": "7305e893875398c5baa585d435eed4e9425cb0dcfa6b76d5d81f514317e2ca0c",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-finite-lean",
      "title": "Julia proof companion reference/Lean/Omega/Finite.lean",
      "filename": "Finite.lean",
      "path": "/julia-proofs/reference/Lean/Omega/Finite.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 2519,
      "sha256": "02bba826557c5206cc168a0eeef6dbd380b69e1892b4b2028e05bdfe6bd53a2d",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-floor-lean",
      "title": "Julia proof companion reference/Lean/Omega/Floor.lean",
      "filename": "Floor.lean",
      "path": "/julia-proofs/reference/Lean/Omega/Floor.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 6808,
      "sha256": "774298bfb89beb990b8bdb6ef0cd95e1cedc7114b2aabf6b1949e91b33a652fb",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-geometry-lean",
      "title": "Julia proof companion reference/Lean/Omega/Geometry.lean",
      "filename": "Geometry.lean",
      "path": "/julia-proofs/reference/Lean/Omega/Geometry.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 6792,
      "sha256": "1cb6284afc2eca467a90de27888d3157aa72cf39ebd788aac505bc256d24638b",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-interface-lean",
      "title": "Julia proof companion reference/Lean/Omega/Interface.lean",
      "filename": "Interface.lean",
      "path": "/julia-proofs/reference/Lean/Omega/Interface.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 4395,
      "sha256": "0a61e038b6c7a8cd42273aacaad53615be8fff13cc43ee61cf798d86ea392ae6",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-ledger-lean",
      "title": "Julia proof companion reference/Lean/Omega/Ledger.lean",
      "filename": "Ledger.lean",
      "path": "/julia-proofs/reference/Lean/Omega/Ledger.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 5377,
      "sha256": "c4c833bd29e349e2550a4c2bfd67d6abe6b76a84a78041d81092f73e6e7d095c",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-main-lean",
      "title": "Julia proof companion reference/Lean/Omega/Main.lean",
      "filename": "Main.lean",
      "path": "/julia-proofs/reference/Lean/Omega/Main.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 1412,
      "sha256": "882556911c03bc06059a80a08a58bc87982dace224591e6368a0ffcad3b06bf8",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-metrics-lean",
      "title": "Julia proof companion reference/Lean/Omega/Metrics.lean",
      "filename": "Metrics.lean",
      "path": "/julia-proofs/reference/Lean/Omega/Metrics.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 2091,
      "sha256": "7715cf5d450e3d166858991f44c75a88ba67a8d3826789d9392cb0e7c32d7b0f",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-placement-lean",
      "title": "Julia proof companion reference/Lean/Omega/Placement.lean",
      "filename": "Placement.lean",
      "path": "/julia-proofs/reference/Lean/Omega/Placement.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 3424,
      "sha256": "6f4d106c949af1f9f12fe25f1a6cfe8a3691af58e3b2ecc26c0782d155690cb2",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-omega-lean",
      "title": "Julia proof companion reference/Lean/Omega.lean",
      "filename": "Omega.lean",
      "path": "/julia-proofs/reference/Lean/Omega.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 18,
      "sha256": "75e6164d192d8f659be9b73da00cb847017e9909631c93596b40d7ee4fad2010",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-proof_guide-md",
      "title": "Julia proof companion reference/Lean/PROOF_GUIDE.md",
      "filename": "PROOF_GUIDE.md",
      "path": "/julia-proofs/reference/Lean/PROOF_GUIDE.md",
      "language": "Markdown",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 10570,
      "sha256": "c2accf70d8b425f6e660724c5df93f1f3521299158566f77fbc585aa1f71e51d",
      "claim_ids": [
        "julia-proof-companion"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "julia-proof-reference-lean-readme-md",
      "title": "Julia proof companion reference/Lean/README.md",
      "filename": "README.md",
      "path": "/julia-proofs/reference/Lean/README.md",
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      "path": "/julia-proofs/reference/Lean/REPRODUCTION.md",
      "language": "Markdown",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "filename": "SHA256SUMS",
      "path": "/julia-proofs/reference/Lean/SHA256SUMS",
      "language": "text",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "id": "julia-proof-reference-lean-source_mapping-md",
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      "filename": "SOURCE_MAPPING.md",
      "path": "/julia-proofs/reference/Lean/SOURCE_MAPPING.md",
      "language": "Markdown",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "title": "Julia proof companion reference/Lean/evidence/axioms.log",
      "filename": "axioms.log",
      "path": "/julia-proofs/reference/Lean/evidence/axioms.log",
      "language": "text",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "filename": "build.log",
      "path": "/julia-proofs/reference/Lean/evidence/build.log",
      "language": "text",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "id": "julia-proof-reference-lean-evidence-setup_lake_update-log",
      "title": "Julia proof companion reference/Lean/evidence/setup_lake_update.log",
      "filename": "setup_lake_update.log",
      "path": "/julia-proofs/reference/Lean/evidence/setup_lake_update.log",
      "language": "text",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "title": "Julia proof companion reference/Lean/lake-manifest.json",
      "filename": "lake-manifest.json",
      "path": "/julia-proofs/reference/Lean/lake-manifest.json",
      "language": "JSON",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "id": "julia-proof-reference-lean-lakefile-lean",
      "title": "Julia proof companion reference/Lean/lakefile.lean",
      "filename": "lakefile.lean",
      "path": "/julia-proofs/reference/Lean/lakefile.lean",
      "language": "Lean",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "id": "julia-proof-reference-lean-lean-toolchain",
      "title": "Julia proof companion reference/Lean/lean-toolchain",
      "filename": "lean-toolchain",
      "path": "/julia-proofs/reference/Lean/lean-toolchain",
      "language": "text",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "id": "julia-proof-reference-lean-scripts-check_axioms-py",
      "title": "Julia proof companion reference/Lean/scripts/check_axioms.py",
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      "path": "/julia-proofs/reference/Lean/scripts/check_axioms.py",
      "language": "Python 3",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "title": "Julia proof companion reference/Lean/scripts/lean_local.sh",
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      "path": "/julia-proofs/reference/Lean/scripts/lean_local.sh",
      "language": "shell",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "in_frozen_g6_release": false
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      "id": "julia-proof-reference-lean-scripts-self_exe-c",
      "title": "Julia proof companion reference/Lean/scripts/self_exe.c",
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      "path": "/julia-proofs/reference/Lean/scripts/self_exe.c",
      "language": "C",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "path": "/julia-proofs/reference/Lean/scripts/verify.sh",
      "language": "shell",
      "runtime_note": "Byte-identical to the overlapping hosted /formal/ file. Lean evidence remains separately identified. OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "in_frozen_g6_release": false
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      "path": "/julia-proofs/run_proofs.jl",
      "language": "Julia",
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      "path": "/julia-proofs/scripts/check_inventory.jl",
      "language": "Julia",
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      "path": "/julia-proofs/scripts/export_guides.jl",
      "language": "Julia",
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      "language": "Julia",
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      "path": "/julia-proofs/src/Dynamics.jl",
      "language": "Julia",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "path": "/julia-proofs/src/ExactArithmetic.jl",
      "language": "Julia",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "filename": "Geometry.jl",
      "path": "/julia-proofs/src/Geometry.jl",
      "language": "Julia",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "path": "/julia-proofs/src/OmegaNaughtProofs.jl",
      "language": "Julia",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
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      "in_frozen_g6_release": false
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      "title": "Polynomial normalizer",
      "filename": "PolynomialCertificates.jl",
      "path": "/julia-proofs/src/PolynomialCertificates.jl",
      "language": "Julia",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 7625,
      "sha256": "01bc9164c584fb87adef800cfa10ccc8c0cafea3e5241c663b1bf95bdf4aa91d",
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      "in_frozen_g6_release": false
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      "path": "/julia-proofs/src/ProofGuide.jl",
      "language": "Julia",
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      "sha256": "4e98dd719a6f792b2490eccc27fe66966a2de8020bd9c2dd61929a4780f95af8",
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      "in_frozen_g6_release": false
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      "filename": "Verification.jl",
      "path": "/julia-proofs/src/Verification.jl",
      "language": "Julia",
      "runtime_note": "OMEGA NAUGHT Julia proof companion v0.1 / OmegaNaughtProofs 0.1.0. Recovered from the Word transcription; SHA-256 matches SHA256SUMS. Author-supplied Julia 1.11.6 O0/O3 records are archived evidence, not a site run. Not an eighth source paper and not a joining theorem. Does not supply cubature 10–21 or 23–24 payloads.",
      "bytes": 22681,
      "sha256": "972dd8e9b4aee7f0101c8010935898a3b8e7fd316e99f3a863b30926049308b5",
      "claim_ids": [
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      "in_frozen_g6_release": false
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      "id": "software-dependencies-docx",
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      "filename": "OMEGA_NAUGHT_Software_Dependencies.docx",
      "path": "/docs/OMEGA_NAUGHT_Software_Dependencies.docx",
      "language": "Word",
      "runtime_note": "Setup instructions and complete text of eleven declaration and lock files, checked 12 September 2026. SHA-256 of this file is of the hosted Word bytes. Loading the document does not install runtimes. Not an eighth source paper and not a joining theorem.",
      "bytes": 45009,
      "sha256": "3841413fe7bfa987b5f394cc526365814fd41381a0241729ace5098ffb1c621e",
      "claim_ids": [],
      "in_frozen_g6_release": false
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      "path": "/cubature/ClassI_Cubature_f23_f24_exact_certificate_v1.1.json",
      "language": "JSON",
      "runtime_note": "Recovered original bytes. SHA-256 matches the published audit pin e886510e… / 41d83727… / 4d56dc2c…. Python 3.11.2 replay_recovered.py PASS on this archive 2026-09-13. python3 -O refused. Does not enlarge Paper VI. No maximality. Not peer review. Not independent third-party reproduction. Distinct from the printed audit extract and from the LaTeX-emitted JSON 3ecbf665….",
      "bytes": 1407835,
      "sha256": "e886510ec03afe014ad143d6d0b45677fc2bb58a7df495374b5780cf79d5b5af",
      "claim_ids": [
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        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f23-f24-verifier",
      "title": "Exact verifier for the f=23,24 certificate",
      "filename": "verify_ClassI_f23_f24_exact_v1.1.py",
      "path": "/cubature/verify_ClassI_f23_f24_exact_v1.1.py",
      "language": "Python 3",
      "runtime_note": "Unchanged historical verifier. Assertions. Requires Python 3.11+. Pass the certificate filename. Do not run with python3 -O. Use replay_recovered.py. Recovered original bytes. SHA-256 matches the published audit pin e886510e… / 41d83727… / 4d56dc2c…. Python 3.11.2 replay_recovered.py PASS on this archive 2026-09-13. python3 -O refused. Does not enlarge Paper VI. No maximality. Not peer review. Not independent third-party reproduction. Distinct from the printed audit extract and from the LaTeX-emitted JSON 3ecbf665….",
      "bytes": 6818,
      "sha256": "41d83727473850ebfbe0bbea0f57f38a64c08d9849170a880b23163769509ce1",
      "claim_ids": [
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f23-f24-ledger",
      "title": "109-row exact residual ledger for f=23,24",
      "filename": "ClassI_Cubature_f23_f24_verification_ledger_v1.1.txt",
      "path": "/cubature/ClassI_Cubature_f23_f24_verification_ledger_v1.1.txt",
      "language": "text",
      "runtime_note": "Recovered original bytes. SHA-256 matches the published audit pin e886510e… / 41d83727… / 4d56dc2c…. Python 3.11.2 replay_recovered.py PASS on this archive 2026-09-13. python3 -O refused. Does not enlarge Paper VI. No maximality. Not peer review. Not independent third-party reproduction. Distinct from the printed audit extract and from the LaTeX-emitted JSON 3ecbf665….",
      "bytes": 10905,
      "sha256": "4d56dc2c65466fc89e6c275fdc38012dbca2c5b74456cf045e7ceedb30a38e6e",
      "claim_ids": [
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f23-f24-replay-launcher",
      "title": "Guarded launcher for the recovered f=23,24 verifier",
      "filename": "replay_recovered.py",
      "path": "/cubature/replay_recovered.py",
      "language": "Python 3",
      "runtime_note": "Recovery support, not part of the historical payload. Hash-pins the three originals and refuses optimized Python. Recovered original bytes. SHA-256 matches the published audit pin e886510e… / 41d83727… / 4d56dc2c…. Python 3.11.2 replay_recovered.py PASS on this archive 2026-09-13. python3 -O refused. Does not enlarge Paper VI. No maximality. Not peer review. Not independent third-party reproduction. Distinct from the printed audit extract and from the LaTeX-emitted JSON 3ecbf665….",
      "bytes": 1621,
      "sha256": "a3bf98e765f18d32f4ac10867c4e914269c61a763d0f7e0b2d1a236b5f41355a",
      "claim_ids": [
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f23-f24-certificate-from-tex",
      "title": "LaTeX-emitted f=23,24 certificate (different bytes)",
      "filename": "ClassI_Cubature_f23_f24_exact_certificate_from_tex_v1.1.json",
      "path": "/cubature/ClassI_Cubature_f23_f24_exact_certificate_from_tex_v1.1.json",
      "language": "JSON",
      "runtime_note": "Mathematically identical contents, different formatting. SHA-256 3ecbf665…. Do not substitute for the original e886510e… certificate.",
      "bytes": 1424503,
      "sha256": "3ecbf6656eee22044f1a9cdaf84e9a3e7365622dcd4d4a1734a1b7c83e15d72b",
      "claim_ids": [
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f2-f21-exact-certificate",
      "title": "Exact Q(sqrt(5)) certificates for f=2 through f=21",
      "filename": "classI_exact_certificates_f2_f21.json",
      "path": "/cubature/classI_exact_certificates_f2_f21.json",
      "language": "JSON",
      "runtime_note": "Recovered archived 2026-08-22 output; original bytes preserved. Python 3.11.2 verify_classI_f2_f21.r2.py PASS on this archive 2026-09-13: 20 frequencies, 383 identities, 404 positive masses. Historical verifier unmodified (assertions). r2 is the recovery revision. Does not enlarge Paper VI. No maximality. Not peer review. Not independent third-party reproduction.",
      "bytes": 1815267,
      "sha256": "7b3945ad58b76341bbc22e7812a359f64b61a68d413b2668012dc155803edb5e",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f2-f21-verifier",
      "title": "Historical exact verifier for f=2 through f=21",
      "filename": "verify_classI_f2_f21.py",
      "path": "/cubature/verify_classI_f2_f21.py",
      "language": "Python 3",
      "runtime_note": "Unmodified historical source. Assertions and floating minimum display retained. Do not run with python3 -O. Recovered archived 2026-08-22 output; original bytes preserved. Python 3.11.2 verify_classI_f2_f21.r2.py PASS on this archive 2026-09-13: 20 frequencies, 383 identities, 404 positive masses. Historical verifier unmodified (assertions). r2 is the recovery revision. Does not enlarge Paper VI. No maximality. Not peer review. Not independent third-party reproduction.",
      "bytes": 4102,
      "sha256": "7c3cd105dae6cf36fd140a8b6525ed722fb02b88bd2ba152c465847befa944fa",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f2-f21-verifier-r2",
      "title": "Recovery revision r2 of the f=2 through f=21 verifier",
      "filename": "verify_classI_f2_f21.r2.py",
      "path": "/cubature/verify_classI_f2_f21.r2.py",
      "language": "Python 3",
      "runtime_note": "Recovery revision. Explicit checks remain active under python3 -O. Reconstructs canonical generators, checks orbit coverage, exact minima, and writes a row ledger. Historical source retained separately. Recovered archived 2026-08-22 output; original bytes preserved. Python 3.11.2 verify_classI_f2_f21.r2.py PASS on this archive 2026-09-13: 20 frequencies, 383 identities, 404 positive masses. Historical verifier unmodified (assertions). r2 is the recovery revision. Does not enlarge Paper VI. No maximality. Not peer review. Not independent third-party reproduction.",
      "bytes": 11383,
      "sha256": "4af07ac2ba14540dfb230920f108cddd0b21e8e80dd2e61dadb79acaad64d7df",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f2-f21-dossier-pdf",
      "title": "Source dossier PDF for the recovered f=2 through f=21 certificates",
      "filename": "ClassI_Cubature_Proof_Dossier_f2_f21.pdf",
      "path": "/cubature/ClassI_Cubature_Proof_Dossier_f2_f21.pdf",
      "language": "PDF",
      "runtime_note": "Recovered original PDF from the archived 22 August 2026 output. Not Paper VI. Recovered archived 2026-08-22 output; original bytes preserved. Python 3.11.2 verify_classI_f2_f21.r2.py PASS on this archive 2026-09-13: 20 frequencies, 383 identities, 404 positive masses. Historical verifier unmodified (assertions). r2 is the recovery revision. Does not enlarge Paper VI. No maximality. Not peer review. Not independent third-party reproduction.",
      "bytes": 226725,
      "sha256": "4c705abab8b99ae50a80c30c497dcd8dbe2170eb37f8c877908de7316c4a31d5",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f2-f21-dossier-tex",
      "title": "Source dossier TeX for the recovered f=2 through f=21 certificates",
      "filename": "ClassI_Cubature_Proof_Dossier_f2_f21.tex",
      "path": "/cubature/ClassI_Cubature_Proof_Dossier_f2_f21.tex",
      "language": "TeX",
      "runtime_note": "Recovered original TeX. Not Paper VI. Recovered archived 2026-08-22 output; original bytes preserved. Python 3.11.2 verify_classI_f2_f21.r2.py PASS on this archive 2026-09-13: 20 frequencies, 383 identities, 404 positive masses. Historical verifier unmodified (assertions). r2 is the recovery revision. Does not enlarge Paper VI. No maximality. Not peer review. Not independent third-party reproduction.",
      "bytes": 9529,
      "sha256": "ee6bd358dbb5a7472b5af9d0c80c5ac7e78dd11811c6201cfc609a2a9119a6fd",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-run-all-recovered",
      "title": "Combined recovered-package launcher",
      "filename": "run_all_recovered.py",
      "path": "/cubature/run_all_recovered.py",
      "language": "Python 3",
      "runtime_note": "Verifies SHA256SUMS then runs f2-21 r2 and f23/f24 replay_recovered.py. Refuses optimized Python and Python < 3.11. Not an independent prover.",
      "bytes": 2552,
      "sha256": "c8549f6be43211b77ccaf6e65aca216e848d5ab563e973760ad73054e537da84",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21",
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-recovered-sha256sums",
      "title": "SHA256SUMS of the 74-file recovered cubature package",
      "filename": "SHA256SUMS",
      "path": "/cubature/evidence/2026-09-13-word-recovery/SHA256SUMS",
      "language": "text",
      "runtime_note": "Original recovered-package manifest. 8322 bytes, SHA-256 71d9d4ac…. Author package inventory, not a this-archive execution.",
      "bytes": 8322,
      "sha256": "71d9d4acb390d8b6f95f411c539e2bc8c7c853b93dc41e4f89f30add71451e07",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21",
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-recovered-evidence-index",
      "title": "Evidence index of the recovered cubature package",
      "filename": "EVIDENCE_INDEX.json",
      "path": "/cubature/evidence/2026-09-13-word-recovery/EVIDENCE_INDEX.json",
      "language": "JSON",
      "runtime_note": "Author package index dated 2026-09-13T17:59:16Z. Distinct from this-archive ENVIRONMENT.json.",
      "bytes": 1438,
      "sha256": "88e97a4befecc44a685ecfcbf195d9f43c9ecd0843d40475099fc5c39c481887",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21",
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-word-extractor",
      "title": "Word extractor used to recover the 74-file cubature package",
      "filename": "extract_omega_word.py",
      "path": "/cubature/evidence/2026-09-13-word-recovery/extract_omega_word.py",
      "language": "Python 3",
      "runtime_note": "Reads EvidenceRecord/EvidenceData/EvidenceEnd styles from word/document.xml. Standard library only. Not one of the 74 original files.",
      "bytes": 3492,
      "sha256": "c4f29970dabe9ee779a7f5d5ed24128d5a75f31b4df36c6d9a7e0d1a847dc6ba",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21",
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-complete-data-docx",
      "title": "Word transport of the 74-file recovered cubature package",
      "filename": "OMEGA_NAUGHT_Complete_Data.docx",
      "path": "/cubature/evidence/2026-09-13-word-recovery/OMEGA_NAUGHT_Complete_Data.docx",
      "language": "DOCX",
      "runtime_note": "Visible-text transport of all 74 original files. SHA-256 279eacb0…. Not an eighth source paper.",
      "bytes": 3721530,
      "sha256": "279eacb0d28cef4a191c7fb733e4eb3b71174b50eb0d902b5364c09fa40d2b6b",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21",
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-this-archive-environment",
      "title": "This-archive Python 3.11.2 cubature recovery environment",
      "filename": "ENVIRONMENT.json",
      "path": "/cubature/evidence/2026-09-13-this-archive/ENVIRONMENT.json",
      "language": "JSON",
      "runtime_note": "pass_on_this_archive. Distinct from author-supplied evidence_* transcripts. Not independently_run and not independent third-party reproduction.",
      "bytes": 5603,
      "sha256": "2146f5d83f01ea714e44677b53436aa4910192b95a2257cea235aa9bab27d21f",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21",
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-this-archive-combined-stdout",
      "title": "This-archive combined cubature stdout",
      "filename": "combined.stdout.txt",
      "path": "/cubature/evidence/2026-09-13-this-archive/combined.stdout.txt",
      "language": "text",
      "runtime_note": "Concatenation of this-archive f2-21 r2 and f23/f24 replay stdout plus COMBINED PASS line. Python 3.11.2.",
      "bytes": 2139,
      "sha256": "e3cf27ae2d7b1951e6567eb16cb022ae7d15a9c51098080a0f5c5ec663b787d4",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21",
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-this-archive-runs",
      "title": "This-archive cubature command records",
      "filename": "runs.json",
      "path": "/cubature/evidence/2026-09-13-this-archive/runs.json",
      "language": "JSON",
      "runtime_note": "Commands, UTC start times, durations, and exit codes for this-archive r2, replay, -O refuse, and historical verifier.",
      "bytes": 2720,
      "sha256": "6dc6c726645fb91758702d3325a382f847679b65bfbe0c80155eeb3f3d8954f5",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21",
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-this-archive-f2-f21-ledger",
      "title": "This-archive r2 row ledger for f=2 through f=21",
      "filename": "f2_f21_ledger.json",
      "path": "/cubature/evidence/2026-09-13-this-archive/f2_f21_ledger.json",
      "language": "JSON",
      "runtime_note": "Written by verify_classI_f2_f21.r2.py on this archive. Distinct from author r2_ledger.json.",
      "bytes": 251693,
      "sha256": "d572ea3ecd53b979fc999ed7f9d2a23fc8b001f5e94a61bcbc6545641c45ac6f",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-this-archive-f2-f21-stdout",
      "title": "This-archive r2 stdout for f=2 through f=21",
      "filename": "f2_f21.stdout.txt",
      "path": "/cubature/evidence/2026-09-13-this-archive/f2_f21.stdout.txt",
      "language": "text",
      "runtime_note": "Python 3.11.2 verify_classI_f2_f21.r2.py ALL PASS. 383 identities. Byte-identical to author r2_normal.stdout.txt.",
      "bytes": 1589,
      "sha256": "4a6474dc9eee66e87a0f6611e0cdb2a9bc53782664f6d8772a3900ca95999b1c",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10",
        "cubature-f11",
        "cubature-f12",
        "cubature-f13",
        "cubature-f14",
        "cubature-f15",
        "cubature-f16",
        "cubature-f17",
        "cubature-f18",
        "cubature-f19",
        "cubature-f20",
        "cubature-f21"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-this-archive-f23-f24-stdout",
      "title": "This-archive replay stdout for f=23 and f=24",
      "filename": "f23_f24.stdout.txt",
      "path": "/cubature/evidence/2026-09-13-this-archive/f23_f24.stdout.txt",
      "language": "text",
      "runtime_note": "Python 3.11.2 replay_recovered.py ALL PASS. 109 identities. certificate_sha256 e886510e…. Byte-identical to author replay.stdout.txt.",
      "bytes": 469,
      "sha256": "7c8bc9622ac5142a4b21d1a8e8897349736a72bf283c66b8f01b5d45d8a5e4e7",
      "claim_ids": [
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-this-archive-replay-O-refuse",
      "title": "This-archive python3 -O refusal of replay_recovered.py",
      "filename": "replay_O.stderr.txt",
      "path": "/cubature/evidence/2026-09-13-this-archive/replay_O.stderr.txt",
      "language": "text",
      "runtime_note": "Exit 1. REFUSED: optimized Python disables the original verifier's assertions.",
      "bytes": 71,
      "sha256": "b0c187e5dd332a99f8e6730485d3a5eb1020706edb8dc24b5b8cb73ffbc220b9",
      "claim_ids": [
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f10-record",
      "title": "Per-frequency exact record for f=10",
      "filename": "f10.json",
      "path": "/cubature/frequencies/f10.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 10 from the shared combined certificate. Degree 33, 1002 nodes, 14 orbits, 14 moment rows, exact minimum (10, 0, 0). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 14643,
      "sha256": "5a65093ea0dc5bef545a62aec3d36735395841f328e4bf1ca28a7d55663a3c26",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f10"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f11-record",
      "title": "Per-frequency exact record for f=11",
      "filename": "f11.json",
      "path": "/cubature/frequencies/f11.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 11 from the shared combined certificate. Degree 35, 1212 nodes, 16 orbits, 15 moment rows, exact minimum (11, 0, 0). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 29467,
      "sha256": "70e63b50ff5390fb31fc1e3dd2aea3fbfe94dd7ceda9634a3c782495904dc764",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f11"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f12-record",
      "title": "Per-frequency exact record for f=12",
      "filename": "f12.json",
      "path": "/cubature/frequencies/f12.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 12 from the shared combined certificate. Degree 39, 1442 nodes, 19 orbits, 18 moment rows, exact minimum (12, 0, 0). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 23331,
      "sha256": "eb911a5a917ead82382364d5375c77233721ffd9a2ef8bef4c55358723a4a67a",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f12"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f13-record",
      "title": "Per-frequency exact record for f=13",
      "filename": "f13.json",
      "path": "/cubature/frequencies/f13.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 13 from the shared combined certificate. Degree 41, 1692 nodes, 21 orbits, 20 moment rows, exact minimum (13, 0, 0). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 56199,
      "sha256": "33316e54f03f302d7577e9ae8111cb4f88c8731f96d35e53aec8a16b5553c833",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f13"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f14-record",
      "title": "Per-frequency exact record for f=14",
      "filename": "f14.json",
      "path": "/cubature/frequencies/f14.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 14 from the shared combined certificate. Degree 45, 1962 nodes, 24 orbits, 23 moment rows, exact minimum (14, 0, 0). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 54482,
      "sha256": "54062dc9ef0a299d226ab481f6cf7fc0299b42c615ba5b1fd475355500cf273e",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f14"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f15-record",
      "title": "Per-frequency exact record for f=15",
      "filename": "f15.json",
      "path": "/cubature/frequencies/f15.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 15 from the shared combined certificate. Degree 47, 2252 nodes, 27 orbits, 25 moment rows, exact minimum (15, 0, 0). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 94096,
      "sha256": "804637e4a35bfdb30692025d18adde567c0fb4057eabeaa11db9891c75478b9e",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f15"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f16-record",
      "title": "Per-frequency exact record for f=16",
      "filename": "f16.json",
      "path": "/cubature/frequencies/f16.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 16 from the shared combined certificate. Degree 51, 2562 nodes, 30 orbits, 29 moment rows, exact minimum (15, 1, 0). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 96687,
      "sha256": "da9bd0fe283870f0c39ca4e23ff798c2b092532008651e6cd9662007174fd3b9",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f16"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f17-record",
      "title": "Per-frequency exact record for f=17",
      "filename": "f17.json",
      "path": "/cubature/frequencies/f17.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 17 from the shared combined certificate. Degree 53, 2892 nodes, 33 orbits, 31 moment rows, exact minimum (17, 0, 0). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 190395,
      "sha256": "1f8927b62eb29f34443a9e4621dc621229a9c5eaafae4927f39313c4caa2423b",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f17"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f18-record",
      "title": "Per-frequency exact record for f=18",
      "filename": "f18.json",
      "path": "/cubature/frequencies/f18.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 18 from the shared combined certificate. Degree 57, 3242 nodes, 37 orbits, 35 moment rows, exact minimum (18, 0, 0). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 171546,
      "sha256": "27f5a8facb13cdcb4a8fc263441f45b7010b2d9c88bbd7caf66b66fdaa317e6b",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f18"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f19-record",
      "title": "Per-frequency exact record for f=19",
      "filename": "f19.json",
      "path": "/cubature/frequencies/f19.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 19 from the shared combined certificate. Degree 59, 3612 nodes, 40 orbits, 37 moment rows, exact minimum (11, 8, 0). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 340223,
      "sha256": "ab5ce5bcfe62d7c51914a1d49a7815dc144b996590476c024cb63af6afe8db75",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f19"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f20-record",
      "title": "Per-frequency exact record for f=20",
      "filename": "f20.json",
      "path": "/cubature/frequencies/f20.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 20 from the shared combined certificate. Degree 63, 4002 nodes, 44 orbits, 42 moment rows, exact minimum (17, 3, 0). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 278192,
      "sha256": "889777fe7b50fd2adb61bbec103609af099650c60080e9b453633fa20b39b384",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f20"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f21-record",
      "title": "Per-frequency exact record for f=21",
      "filename": "f21.json",
      "path": "/cubature/frequencies/f21.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 21 from the shared combined certificate. Degree 65, 4412 nodes, 48 orbits, 44 moment rows, exact minimum (20, 1, 0). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 475270,
      "sha256": "2083b6cd9e02727f1e7999980a4409590cf2100b60d98c92ad9cc10f90db12be",
      "claim_ids": [
        "cubature-f10-f21",
        "cubature-f21"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f23-record",
      "title": "Per-frequency exact record for f=23",
      "filename": "f23.json",
      "path": "/cubature/frequencies/f23.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 23 from the shared combined certificate. Degree 71, 5292 nodes, 56 orbits, 52 moment rows, exact minimum (21, 1, 1). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 773851,
      "sha256": "2681e49031ad840ce9cf544b8ba588d17d21b5b876472cdfc4cf851bf53f356b",
      "claim_ids": [
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "cubature-f24-record",
      "title": "Per-frequency exact record for f=24",
      "filename": "f24.json",
      "path": "/cubature/frequencies/f24.json",
      "language": "JSON",
      "runtime_note": "Derived export of frequency 24 from the shared combined certificate. Degree 75, 5762 nodes, 61 orbits, 57 moment rows, exact minimum (23, 1, 0). Own SHA-256. Does not enlarge Paper VI. No maximality.",
      "bytes": 621792,
      "sha256": "779c0994128af09f109858a1714b9d94959d39d98f1e2671eb3b4cdb781f9658",
      "claim_ids": [
        "cubature-f23-f24-existence",
        "cubature-f23-f24-rank"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "synthesis-claim-check-stdout",
      "title": "This-archive stdout of the Synthesis 1.0 companion checker",
      "filename": "omega_synthesis_claim_check.stdout.txt",
      "path": "/synthesis/omega_synthesis_claim_check.stdout.txt",
      "language": "text",
      "runtime_note": "Python 3.11.2, 2026-09-17T19:30:11Z. Identical stdout in normal, -O, and -OO. ALL FOCUSED CLAIM CHECKS PASS. Not a run of the original synthesis package suite.",
      "bytes": 434,
      "sha256": "a6e768c3be44016a5778817d6bf018c50f91252d578775ae9a2d78b2b0b77f0e",
      "claim_ids": [
        "floor-first-disagreement"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "synthesis-claim-check-env",
      "title": "This-archive environment record for the Synthesis 1.0 checker",
      "filename": "ENVIRONMENT.json",
      "path": "/synthesis/ENVIRONMENT.json",
      "language": "JSON",
      "runtime_note": "Records interpreter, UTC, commands, exit codes, and that OMEGA_Synthesis(3).pdf was not supplied. Claimed PDF SHA-256 01f0d19c… is unverified here.",
      "bytes": 1631,
      "sha256": "a98aee33c39d866613f5d3269a8275a9d28913d921254dad10a2a07fb8d6eb3b",
      "claim_ids": [
        "floor-first-disagreement"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "synthesis-review-md",
      "title": "Written second review of OMEGA Synthesis 1.0",
      "filename": "REVIEW.md",
      "path": "/synthesis/REVIEW.md",
      "language": "Markdown",
      "runtime_note": "Assessment of printed hypotheses and the Farey first-disagreement certificate. Not a source paper. The reviewed PDF was not hosted here.",
      "bytes": 5908,
      "sha256": "f1902ef6987ccda1e5e7967b1d95b8de3cc8bcf867ae5a2137807e6701b670bf",
      "claim_ids": [
        "floor-first-disagreement"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-pdf",
      "title": "OMEGA–Navier–Stokes geometric transport, Extension 1.0 (historical)",
      "filename": "OMEGA_NS_Geometric_Extension.pdf",
      "path": "/extension/v1/OMEGA_NS_Geometric_Extension.pdf",
      "language": "PDF",
      "runtime_note": "Historical local host of Extension 1.0, 18 September 2026. Superseded on this archive by Version 3.0. Not a source paper.",
      "bytes": 395411,
      "sha256": "fc66480bc599f6322c79b08f777e4650b25ce20795f2f1084717c1798faf0d10",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-py",
      "title": "SymPy companion for Extension 1.0 (historical)",
      "filename": "verify_omega_ns.py",
      "path": "/extension/v1/verify_omega_ns.py",
      "language": "Python 3",
      "runtime_note": "Historical 34-check companion. Superseded by Version 3.0 verify_omega_ns.py.",
      "bytes": 6622,
      "sha256": "d6dfd762f98bc2878d60bb06ec2599c211c3ec5535d595e5180d8cfb5082979d",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-stdout",
      "title": "This-archive stdout of Extension 1.0 verifier (historical)",
      "filename": "verify_omega_ns.stdout.txt",
      "path": "/extension/v1/verify_omega_ns.stdout.txt",
      "language": "text",
      "runtime_note": "Python 3.10.21, SymPy 1.14.0, 2026-09-18T03:41:44Z. Identical stdout in normal, -O, and -OO. TOTAL: 34 exact checks.",
      "bytes": 1700,
      "sha256": "e39a48e357a6daa21284b6755a7b1739911f0918cb37d1faf7f8ea02775847e6",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-env",
      "title": "This-archive environment record for Extension 1.0 (historical)",
      "filename": "ENVIRONMENT.json",
      "path": "/extension/v1/ENVIRONMENT.json",
      "language": "JSON",
      "runtime_note": "Interpreter, UTC, commands, exit codes, and explicit non-claims.",
      "bytes": 1420,
      "sha256": "872f370bfc5f04f11b17631b2fc09b298a025a65bc2e41df1985b28f0f9e9050",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-v3-pdf",
      "title": "OMEGA–Navier–Stokes geometric transport, Version 3.0",
      "filename": "OMEGA_NS_Geometric_Extension_v3.pdf",
      "path": "/extension/OMEGA_NS_Geometric_Extension_v3.pdf",
      "language": "PDF",
      "runtime_note": "Received 20-page PDF as hosted. SHA-256 98a3f747… does not match the revision-notes claim 42802e00…. Extra Content Credentials attachment present. Eight intended supplements match the notes. Not a source paper. Not a blowup result.",
      "bytes": 2376354,
      "sha256": "98a3f74742dd3d06626ec03a248e8ce901772c18d836a5e736e1f1e594e6d675",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-v3-tex",
      "title": "Version 3.0 TeX source",
      "filename": "OMEGA_NS_Geometric_Extension.tex",
      "path": "/extension/OMEGA_NS_Geometric_Extension.tex",
      "language": "TeX",
      "runtime_note": "Extracted from the received PDF. SHA-256 matches the revision notes. pdflatex was not rerun here.",
      "bytes": 66020,
      "sha256": "2cadfed871fc74bdf61683b09f0cc9de54aa05ada0df6b7d103f7bd760bd6cf9",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-v3-py",
      "title": "SymPy companion for Version 3.0",
      "filename": "verify_omega_ns.py",
      "path": "/extension/verify_omega_ns.py",
      "language": "Python 3",
      "runtime_note": "62 exact identity checks plus retained integer/rational tests. require() stays active under -O/-OO.",
      "bytes": 18425,
      "sha256": "f054d343f78c96f18d1a4360453dd1761d3fc8de7757edfb56a746996921e531",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-v3-audit",
      "title": "v0.1 source auditor for Version 3.0",
      "filename": "audit_omega_sources.py",
      "path": "/extension/audit_omega_sources.py",
      "language": "Python 3",
      "runtime_note": "Fixed-release auditor. Not a general Julia/Lean interpreter. No fresh Lean or Julia runtime.",
      "bytes": 25344,
      "sha256": "7bb072407b4c2c3ea58c0a8a0ad392d5870fc1d7d339ff20b67679b9ad96f08e",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-v3-harness",
      "title": "Auditor mutation harness for Version 3.0",
      "filename": "test_omega_auditor.py",
      "path": "/extension/test_omega_auditor.py",
      "language": "Python 3",
      "runtime_note": "19 cases (original plus 18 mutations), each in normal and -O.",
      "bytes": 9531,
      "sha256": "9cae8025b0b6637ca5b188b30d84235b3c73a122445f0a7fdd9fcf8df6d5f509",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-v3-build",
      "title": "PDF build script for Version 3.0 (not rerun)",
      "filename": "build_omega_pdf.py",
      "path": "/extension/build_omega_pdf.py",
      "language": "Python 3",
      "runtime_note": "Requires pdflatex and pypdf. Not executed on this archive.",
      "bytes": 3421,
      "sha256": "a08a93700ee779cb9ac2158cd4c27e4124e1b8c069a62c9b8f26cd71f68e3700",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-v3-record",
      "title": "Author Version 3.0 verification record",
      "filename": "OMEGA_V3_Verification_Record.txt",
      "path": "/extension/OMEGA_V3_Verification_Record.txt",
      "language": "text",
      "runtime_note": "Author transcript, Python 3.12.14. Distinct from this-archive runs.",
      "bytes": 14352,
      "sha256": "095d05494a301c1fe21f72df044da569b9a00d01e5edc841bdfe4fe5eed91f01",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-v3-notes",
      "title": "Version 3.0 revision notes",
      "filename": "revision-notes.md",
      "path": "/extension/revision-notes.md",
      "language": "Markdown",
      "runtime_note": "Supplied revision notes. Contains the claimed PDF digest that does not match the received file.",
      "bytes": 7835,
      "sha256": "6f0b510431c632b7994c9da4eb019a98e2c5bf63b69498ab07b742b089acff50",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-v3-stdout",
      "title": "This-archive stdout of verify_omega_ns.py (v3)",
      "filename": "verify_omega_ns.stdout.txt",
      "path": "/extension/verify_omega_ns.stdout.txt",
      "language": "text",
      "runtime_note": "Python 3.11.2, SymPy 1.14.0, 2026-09-19T11:01:17Z. Identical in normal, -O, and -OO.",
      "bytes": 3937,
      "sha256": "6025d715b46ebd288bed3340a19142121a780e38f74dcdbf6b5a47691d6ed2b2",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-v3-audit-stdout",
      "title": "This-archive stdout of audit_omega_sources.py",
      "filename": "audit_omega_sources.stdout.txt",
      "path": "/extension/audit_omega_sources.stdout.txt",
      "language": "text",
      "runtime_note": "Original package accepted. Identical under -O. No fresh Lean or Julia execution.",
      "bytes": 740,
      "sha256": "d0c1d8d8273d0db5ff2ffc2fccaa6139b81569cc88074f1788c04c87ed627677",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-v3-test-stdout",
      "title": "This-archive stdout of test_omega_auditor.py",
      "filename": "test_omega_auditor.stdout.txt",
      "path": "/extension/test_omega_auditor.stdout.txt",
      "language": "text",
      "runtime_note": "38 subprocess checks; 36 required rejections. Python 3.11.2.",
      "bytes": 4229,
      "sha256": "62553e270eea74e8d2e42a44ce48564df7d6f63c676b0a66176ebbd71120bf97",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-v3-env",
      "title": "This-archive environment record for Version 3.0",
      "filename": "ENVIRONMENT.json",
      "path": "/extension/ENVIRONMENT.json",
      "language": "JSON",
      "runtime_note": "Interpreter, UTC, commands, exit codes, PDF hash mismatch, explicit non-claims.",
      "bytes": 3521,
      "sha256": "ebadfe2c417762fd32d19d2391e6ddcccd9111b954c150ce249dc3b1e330b820",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
      "id": "ns-extension-v3-lean-docx",
      "title": "Lean v0.1 DOCX extracted from Version 3.0 PDF",
      "filename": "LEAN_Proof_Complete_Final(1).docx",
      "path": "/extension/sources/LEAN_Proof_Complete_Final(1).docx",
      "language": "DOCX",
      "runtime_note": "SHA-256 275da4ea… matches the already hosted frozen Lean transcription.",
      "bytes": 75151,
      "sha256": "275da4ea14130d21aa1b797b643ec78192e195780bfd8352bac699a75b73542e",
      "claim_ids": [
        "omega-ns-geometric-extension"
      ],
      "in_frozen_g6_release": false
    },
    {
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