{ "schema": "OMEGA_NAUGHT_MACHINE/1.0", "canonical_url": "https://omega-naught.grok.me/archive/MACHINE.json", "site": "https://omega-naught.grok.me", "generated": "2026-10-27", "buildGeneratedAt": "2026-10-27T12:35:55.074Z", "contentUpdatedAt": "2026-10-01", "date_meanings": { "generated": "UTC date this MACHINE.json file was written. Not a proof date and not a deposit date.", "buildGeneratedAt": "UTC timestamp of this index build.", "contentUpdatedAt": "Editorial site date from quality/content-dates.json. Not a proof date, build time, or historical execution date.", "publishedAt": "Deposit or publication date, stored on each source work.", "artifactCreatedAt": "Date of an artifact’s bytes, stored with that artifact when known.", "executionAt": "UTC time of a named checker run, stored in that run’s record." }, "purpose": "Canonical machine entry point for OMEGA NAUGHT. An agent should fetch this file first, then retrieve only the artifacts named on the object it is checking. This is an index of separated evidence, not a joining theorem and not a belief instruction.", "source_works": 8, "source_work_labels": "Papers I–VII (Roman) and paper 8 (Arabic numeral on purpose)", "paper_8": { "id": "paper-8", "path": "/papers/8", "status": "Zenodo preprint retrieved; companion ZIP hosted; this-archive Python replay PASS", "doi": "10.5281/zenodo.22848213", "local_pdf": "/papers/OMEGA_Paper_VIII_Final.pdf", "local_pdf_sha256": "9827d625a33ea797417fb2847fc8db23c46980b870466b5a1e4b0e66a8c63785", "zip": "/papers/8/OMEGA_Paper_VIII_Source_and_Code.zip", "zip_sha256": "cbdf7a29d67942eff0bf839f30fb8071125c5c213a60e8d648f116f07a2c2f75", "checker_sha256": "dbf0650cf80c9e618684d98292bf7592baadadc51bd2eccf15b950392dcd5c8b", "certificate_sha256": "32bcc2fefc44d0fe19575683b64fd67ddcd32327aeff32ab14cc988a507f4a79", "note": "Site label is paper 8, not Paper VIII. Not peer review. Not a Navier–Stokes blowup theorem. Does not enlarge Paper VI. Hosted ZIP cbdf7a29… is the corrected Zenodo release. Review hash 5e47b7d5… is the original submitted archive, a version difference, not a corrupted upload." }, "peer_reviewed": false, "independent_reproduction": { "status": "none-recorded", "records": [] }, "independent_reproduction_note": "A second-language port derived from the same reference implementation does not automatically qualify as independent third-party reproduction. Every recorded reproduction must name a person or group, date, method, and public evidence link.", "software_dependencies": { "id": "software-dependencies-docx", "path": "/docs/OMEGA_NAUGHT_Software_Dependencies.docx", "filename": "OMEGA_NAUGHT_Software_Dependencies.docx", "bytes": 45009, "sha256": "3841413fe7bfa987b5f394cc526365814fd41381a0241729ace5098ffb1c621e", "note": "Setup instructions and complete transcriptions of eleven lock and declaration files. Not an additional source paper and not a joining theorem." }, "frozen_g6": { "contract": "G6_RELEASE/1.1", "path": "/releases/G6_RELEASE_1.1/RELEASE.json", "sha256": "f63ae1c2d595b4805ba9d36687a828fd87200febe01079b184723f7d5eaf746c", "status": "frozen_unarchived", "note": "Historical packaging of Papers I–VI. Unrelated typed objects can always be placed in a tuple. Not a joining theorem and not the current semantic architecture." }, "instructions_for_agents": [ "Start here. Do not infer coordinates, uniqueness, or unification from pictures, HTML chrome, or page adjacency.", "Treat each object as an independent claim axis. Never collapse them into one verified badge.", "implementation_conformance PASS means a named runtime reproduced a named output. It is not theorem validity, peer review, or independent third-party reproduction.", "A Python or Julia PASS is not by itself a Lean kernel-check. lake build PASS on this archive (2026-09-13) is machine-checking of the selected maps in omega_provenance v0.1; it is not peer review of Papers I–VII and not independent third-party reproduction of those papers.", "Cubature does not logically depend on Ω₀ or SRSD.", "SRSD v1.0 is a frozen external audit instrument, not a fifth source theory in the same sense and not a foundation of a combined object.", "Historical G₆ packaging is not a joining theorem.", "paper 8 is a Zenodo preprint at 10.5281/zenodo.22848213. Lean, Julia companion, Construct, typed-network, Omega-Alpha, successor search, training modules, NS extension, fiber handoff, and the software-dependencies transcription do not become paper 8 by adjacency.", "G₆ and OMEGA_NAUGHT/1.0 Rust runners declare no third-party crates. The named Cargo command is cargo run --release --offline --locked. Setup transcription: /docs/OMEGA_NAUGHT_Software_Dependencies.docx.", "The Lean theorem concerns a selected measurement of a specified construction. It does not assert uniqueness among all measurements of an unmarked outline.", "Author-supplied Julia 1.11.6 O0/O3 logs are archived evidence. They are not a run performed on this archive and not a Lean kernel-check.", "The Construct node log transfers the unique labeled planar kernel. It does not transfer a unique outer shell, clam, extrusion, or signed depth.", "Independent third-party reproduction is currently recorded as none.", "Public site exposes no accounts or login." ], "how_to_use": [ "DISCOVER — fetch this contract and /llms.txt", "SELECT OBJECT — pick one named object; never collapse independent claim axes", "READ DEFINITIONS — follow definition_paper or definition_source and page on the chosen object", "IDENTIFY CLAIM SCOPE — read claim_ids, claims_not_made, and evidence_kinds", "FETCH — retrieve path + verify sha256", "RESOLVE ALIASES — certificate-f22-69, certificate-f22-70, and g6-release-1-1 are in source_registry", "RECONSTRUCT OBJECT — for geometry, use the node log and declared constants; do not digitize the figure", "EXECUTE VERIFIER — run execute.commands where present and compare to expected", "FORMALLY CHECK WHERE LEAN EXISTS — lake build PASS on this archive 2026-09-13; transcripts at /formal/evidence/current/; package SHA256SUMS 28/28; toolchain and .lake are not hosted", "JULIA COMPANION — hosted members match SHA256SUMS; do not treat author O0/O3 transcripts as a site run or as lake build", "COMPARE WITH CLAIM — report PASS/FAIL only for the named finite or implementation scope", "REPORT EVIDENCE + LIMITATIONS — keep independent axes independent; do not collapse cubature 10–21, 22, 23–24, or ≥25 into one theorem; Paper VI remains 1≤f≤9" ], "evidence_kinds": { "paper_proof": "Statement and proof in a source preprint or report. Not machine-checked here.", "written_note_proof": "Statement and written proof in a separately identified supplementary note or its dated remarks; not an additional counted source work and not automatically machine-checked.", "lean_source": "Hosted Lean 4 source. Kernel-check is lake build. This archive records pass_on_this_archive for omega_provenance v0.1 on 2026-09-13. That is not independent third-party reproduction of Papers I–VII.", "exact_finite_certificate": "Exact finite or exact-algebraic check with a named expected output.", "implementation_conformance": "Named runtime reproduced a named frozen output.", "construction_record": "Declared constants, nodes, frame, and equations sufficient to rebuild a specified object.", "author_transcript": "Author-supplied log or dump. Not generated on this archive unless a named runtime says otherwise.", "unpackaged": "Author result outside the fully reproducible public corpus.", "open": "Conjecture or incomplete range. Not a theorem on this archive." }, "indexes": { "overview": "/archive/OVERVIEW.md", "llms": "/llms.txt", "claims": "/archive/claims.json", "artifacts": "/archive/artifacts.json", "conformance": "/archive/conformance.json", "papers": "/archive/papers.json", "sitemap": "/sitemap.xml", "citation": "/CITATION.cff", "bibtex": "/citations/omega-naught.bib" }, "source_registry": { "certificate-f22-69": { "resolves_to": "f22-degree69-canonical", "page": "/cubature/f22#degree-69", "note": "Positive degree-69 certificate on fixed X22. Alias used in claim source_ids." }, "certificate-f22-70": { "resolves_to": "f22-degree71-canonical", "page": "/cubature/f22#obstruction", "note": "Degree-70/71 obstruction certificate on fixed X22. Alias used in claim source_ids." }, "g6-release-1-1": { "resolves_to": "g6-release-json", "page": "/integration", "path": "/releases/G6_RELEASE_1.1/RELEASE.json", "note": "Frozen G6_RELEASE/1.1 envelope. Historical packaging, not a joining theorem." }, "boundary-note-2026-09-21": { "resolves_to": "boundary-pdf", "page": "/geometry/boundary-reconstruction", "path": "/geometry/boundary-reconstruction/Boundary_Reconstruction_Transport_Formal_Proof.pdf", "note": "Original 21 September 2026 supplementary proof note. Not an additional counted source work." }, "boundary-remarks-2026-09-22": { "resolves_to": "boundary-remarks", "page": "/geometry/boundary-reconstruction", "path": "/geometry/boundary-reconstruction/REMARKS.md", "note": "Supplementary written proofs of the two-step compatibility, antipodal criterion, and surviving kernel. Not pages of the original PDF." } }, "objects": [ { "id": "omega-marked-kernel", "object": "OMEGA marked planar kernel", "kind": "construction_record", "definition_paper": "paper-vii", "definition": "Paper VII v1.6 Construction-to-OMEGA: one-arcsecond circular seed with bilateral golden extensions. Unique labeled similarity class in an oriented plane.", "page": "/geometry", "claim_ids": [ "geometry-local-closure", "geometry-angular-fan", "geometry-center-relative", "geometry-construct-interface" ], "constants": { "epsilon": "pi/648000", "epsilon_note": "one arcsecond", "phi": "(1+sqrt(5))/2", "levels": [ "-(phi^2+s)", "-(1+s)", "-s", "s", "1+s", "phi^2+s" ] }, "construction": { "schema": "OMEGA_KERNEL_NODES/1.0", "node_log": { "id": "construct-node-log", "path": "/geometry/construct/omega-kernel-nodes.unit.true.json", "filename": "omega-kernel-nodes.unit.true.json", "bytes": 5456, "sha256": "f821ada8c166d5f8fe00fee6d3d978fae514862c504f0b5bc355d0f3cecb6f8c" }, "kernel_json": { "id": "paper-vii-kernel-json", "path": "/geometry/kernel/OMEGA_local_kernel_v1_6_0.json", "filename": "OMEGA_local_kernel_v1_6_0.json", "bytes": 4281, "sha256": "b280522bcd2cf63927e8dfd6438f78fa3a2e7af0cbfd484ee9cd55994b9c3753" }, "generator": { "id": "paper-vii-kernel-py", "path": "/geometry/kernel/omega_reference_geometry.py", "filename": "omega_reference_geometry.py", "bytes": 10096, "sha256": "5151dcac227eae510dbcf26f0815c39e8ab66ef54482d8973c93347008117489" }, "verifier": { "id": "paper-vii-kernel-verify", "path": "/geometry/kernel/verify_geometry.py", "filename": "verify_geometry.py", "bytes": 7860, "sha256": "140a957e3c5bb26f3c88eefdfc21b4bceac132900b07cc2ef14aa03b702ffcae" }, "julia_realization": { "id": "paper-vii-kernel-jl", "path": "/geometry/kernel/omega_kernel_oriented_r3.jl", "filename": "omega_kernel_oriented_r3.jl", "bytes": 6235, "sha256": "760162f6470fde51c95cf30cca459e2e160825d73e790a46dc4580aca588d47c" } }, "execute": { "cwd_hint": "geometry/kernel", "commands": [ "mkdir -p generated regenerated", "python3 -m pip install numpy", "python3 verify_geometry.py", "python3 omega_reference_geometry.py --json regenerated/OMEGA_local_kernel_v1_6_0.json --obj regenerated/OMEGA_local_kernel_v1_6_0.obj" ], "expected": "Eight numerical conformance groups PASS, including distributed-export comparison against generated/. Independent generation writes regenerated copies. Not a theorem checker for Paper VII. Optional Julia Plots visualization is a separate environment." }, "formalization": { "package": "omega_provenance/0.1", "modules": [ "/formal/Omega/Geometry.lean", "/formal/Omega/Placement.lean", "/formal/Omega/Constants.lean" ], "note": "Lean takes this construction as an input to a selected measurement. It does not prove the construction is the only possible measurement of an unmarked outline." }, "evidence_kinds": [ "paper_proof", "construction_record" ], "independent_of": [ "class-i-cubature", "legacy-g6" ], "claims_not_made": [ "unique outer shell, clam, extrusion, or signed depth", "joining theorem with Papers I–VI", "peer review", "independent third-party reproduction" ] }, { "id": "construct-transfer-gate", "object": "Construct mode transfer record of the marked kernel", "kind": "construction_record", "definition_paper": "paper-vii", "definition": "OMEGA Kernel Construct v1.1.0. Fifteen sourced presentation stages. Node-log export is the transfer payload another system may use to rebuild the unique labeled planar kernel in R³.", "page": "/geometry#shape", "claim_ids": [ "geometry-construct-interface" ], "construction": { "schema": "OMEGA_KERNEL_NODES/1.0", "node_log": { "id": "construct-node-log", "path": "/geometry/construct/omega-kernel-nodes.unit.true.json", "filename": "omega-kernel-nodes.unit.true.json", "bytes": 5456, "sha256": "f821ada8c166d5f8fe00fee6d3d978fae514862c504f0b5bc355d0f3cecb6f8c" }, "technical_paper": { "id": "construct-paper-pdf", "path": "/geometry/construct/OMEGA_Kernel_Construct_v1.1.0.pdf", "filename": "OMEGA_Kernel_Construct_v1.1.0.pdf", "bytes": 368491, "sha256": "6b2593e2ad232793296b8e8b3acadcc8a71d240b5e8c799342d90cd1815bd912" }, "scalar_certificate": { "id": "construct-scalar-py", "path": "/geometry/construct/verify_scalar_interface_exact.py", "filename": "verify_scalar_interface_exact.py", "bytes": 7716, "sha256": "863d1b2166a4264aeec7aba72faedd7136b3f4a5d9405e9e9111b6df7617b387" }, "display_exaggeration": "12° picture is display-only; true epsilon is one arcsecond and is what the node log carries" }, "execute": { "cwd_hint": "geometry/construct", "commands": [ "python3 verify_scalar_interface_exact.py" ], "expected": "OMEGA scalar interface exact algebra certificate: PASS" }, "evidence_kinds": [ "construction_record", "exact_finite_certificate" ], "may_pass": [ "kernel data in OMEGA_KERNEL_NODES/1.0" ], "may_pass_only_if_adopted": [ "metric outer scaffold S, E, L" ], "does_not_travel": [ "outer_circle", "clam", "shell", "extrusion", "signed_depth", "12° display coordinates" ], "claims_not_made": [ "unique 3D shell", "Paper VII Euclidean uniqueness via the Python scalar certificate", "joining theorem", "additional source paper" ] }, { "id": "geometric-provenance-lean", "object": "Selected geometric-provenance measurement (Lean 4)", "kind": "lean_source", "definition_paper": "paper-vii", "definition": "Selected golden readout G = average of the two outer segment lengths = a φ. Selected circular readout C = opposite-semicircle length = a π. W = G+C. T(x) = 1+λ(x-1), λ = φ/(φ+π). Construction and measurement rule are explicit inputs.", "page": "/formal", "claim_ids": [ "lean-provenance-formalization" ], "main_theorem": "Omega.central_provenance_theorem", "main_theorem_path": "/formal/Omega/Main.lean", "package": { "name": "omega_provenance", "version": "0.1", "lean": "4.19.0", "lean_commit": "6caaee842e94", "mathlib": "v4.19.0", "mathlib_commit": "c44e0c8ee63ca166450922a373c7409c5d26b00b" }, "modules": { "Constants": "/formal/Omega/Constants.lean", "Geometry": "/formal/Omega/Geometry.lean", "Placement": "/formal/Omega/Placement.lean", "Affine": "/formal/Omega/Affine.lean", "Dimension": "/formal/Omega/Dimension.lean", "Floor": "/formal/Omega/Floor.lean", "Finite": "/formal/Omega/Finite.lean", "Extinction": "/formal/Omega/Extinction.lean", "Ledger": "/formal/Omega/Ledger.lean", "Interface": "/formal/Omega/Interface.lean", "Metrics": "/formal/Omega/Metrics.lean", "Main": "/formal/Omega/Main.lean", "AxiomAudit": "/formal/Omega/AxiomAudit.lean" }, "dependency_chain": [ "Constants/Geometry/Placement", "geometric provenance (G=aφ, C=aπ)", "Affine (T and homothety)", "finite floor equality on D={0,...,32767}", "Ledger reconstruction", "Omega.central_provenance_theorem" ], "artifacts": { "main": { "id": "lean-omega-main", "path": "/formal/Omega/Main.lean", "filename": "Main.lean", "bytes": 1412, "sha256": "882556911c03bc06059a80a08a58bc87982dace224591e6368a0ffcad3b06bf8" }, "sha256sums": { "id": "lean-sha256sums", "path": "/formal/SHA256SUMS", "filename": "SHA256SUMS", "bytes": 2373, "sha256": "f8208d18f6ac80dfbd4a7b73eec7bb865820e1c703717ee47bf1704ed0258e81" }, "lakefile": { "id": "lean-lakefile", "path": "/formal/lakefile.lean", "filename": "lakefile.lean", "bytes": 238, "sha256": "30e552cd01e0b82081a26f9446cab1960f1f157f9c120a86740fa3656eb56e5c" }, "toolchain": { "id": "lean-toolchain", "path": "/formal/lean-toolchain", "filename": "lean-toolchain", "bytes": 25, "sha256": "55e97be96000b5e9e290c9e74482e5e317861499a5540353ce845471bded8cea" }, "readme": { "id": "lean-readme", "path": "/formal/README.md", "filename": "README.md", "bytes": 5963, "sha256": "1396da8c8cd39227588d260b4086f1f7ae3aeec2f319251cb8e7879802986643" }, "proof_guide": { "id": "lean-proof-guide", "path": "/formal/PROOF_GUIDE.md", "filename": "PROOF_GUIDE.md", "bytes": 10570, "sha256": "c2accf70d8b425f6e660724c5df93f1f3521299158566f77fbc585aa1f71e51d" }, "source_mapping": { "id": "lean-source-mapping", "path": "/formal/SOURCE_MAPPING.md", "filename": "SOURCE_MAPPING.md", "bytes": 4511, "sha256": "35122d4222988b074ab80e46316c050ab1b17d2047248396bbcce3489819ffd7" }, "axioms_log": { "id": "lean-axioms-log", "path": "/formal/evidence/axioms.log", "filename": "axioms.log", "bytes": 11804, "sha256": "82dae0644b5ce591c3e4af7bf9fdbfa6aeec11591560cb785ab0727a65d8eda1" }, "check_axioms": { "id": "lean-check-axioms", "path": "/formal/scripts/check_axioms.py", "filename": "check_axioms.py", "bytes": 1326, "sha256": "f57f46411b7245ec715eb13e4546d82d273eb9a8bbfe186c9f4fbf07fe78f5c2" }, "check_axioms_runtime": { "id": "lean-check-axioms-runtime", "path": "/formal/check_axioms.runtime.txt", "filename": "check_axioms.runtime.txt", "bytes": 926, "sha256": "f0f843b744e7d04fb8e764c88f021ef93c03a8b85e2f8a1d4d29d2ef8d1868c8" }, "lake_build_log": { "id": "lean-lake-build-log", "path": "/formal/evidence/current/build.log", "filename": "build.log", "bytes": 1960, "sha256": "ddc10580b76d0dd4ec8d9012bf91a78338fc43c003c4f7dbab2421f3c2b760b9" }, "lake_axioms_log": { "id": "lean-lake-axioms-log", "path": "/formal/evidence/current/axioms.log", "filename": "axioms.log", "bytes": 11804, "sha256": "82dae0644b5ce591c3e4af7bf9fdbfa6aeec11591560cb785ab0727a65d8eda1" }, "lake_environment": { "id": "lean-lake-environment", "path": "/formal/evidence/current/ENVIRONMENT.json", "filename": "ENVIRONMENT.json", "bytes": 9793, "sha256": "622ce56958f1dce7e28a26615c618313dc7d62046932301cdac06880ba7000ff" }, "sorry_scan": { "id": "lean-sorry-scan", "path": "/formal/evidence/current/sorry_scan.txt", "filename": "sorry_scan.txt", "bytes": 1610, "sha256": "58b5ac839405753ff6df9434f716cf12b9f4f9d61f59f8e7333fa2577523ed69" }, "lake_check_axioms_runtime": { "id": "lean-lake-check-axioms-runtime", "path": "/formal/evidence/current/check_axioms.runtime.txt", "filename": "check_axioms.runtime.txt", "bytes": 1226, "sha256": "e10e6ea8c8bdd6c78a82a5b734359126e96e8e60106425f418943b6ba25af884" }, "lake_current_sha256sums": { "id": "lean-lake-current-sha256sums", "path": "/formal/evidence/current/SHA256SUMS", "filename": "SHA256SUMS", "bytes": 408, "sha256": "c6eb2c9233b8da93d9d91f541c5b2f35d0a567bd360d091d4e4f8828fff01bae" } }, "build_status": "pass_on_this_archive", "lake_build": "pass_on_this_archive", "python_axiom_coverage": { "status": "pass", "runtime": "Python 3.10.21", "command": "python3 scripts/check_axioms.py evidence/current/axioms.log", "expected": "Checked 147 theorem reports; axioms: Classical.choice, Quot.sound, propext", "expected_output_ref": "/formal/evidence/current/check_axioms.runtime.txt", "note": "Inventory of the 2026-09-13 axiom report against hosted theorem names. The current axioms.log is byte-identical to the author log. Not a proof oracle." }, "lake_run": { "status": "pass_on_this_archive", "date": "2026-09-13", "lean": "4.19.0", "lean_commit": "6caaee842e94", "lake": "5.0.0-6caaee8", "mathlib": "v4.19.0", "mathlib_commit": "c44e0c8ee63ca166450922a373c7409c5d26b00b", "os": "Linux 6.12.8+ x86_64", "python": "Python 3.10.21", "ld_preload": "self_exe.so compiled from hosted scripts/self_exe.c; executable discovery only", "toolchain_hosted": false, "lake_cache_hosted": false, "theorems": 147, "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "axiom_free_theorems": 4, "sorry_admit_native_decide": 0, "build_log": { "id": "lean-lake-build-log", "path": "/formal/evidence/current/build.log", "filename": "build.log", "bytes": 1960, "sha256": "ddc10580b76d0dd4ec8d9012bf91a78338fc43c003c4f7dbab2421f3c2b760b9" }, "axioms_log": { "id": "lean-lake-axioms-log", "path": "/formal/evidence/current/axioms.log", "filename": "axioms.log", "bytes": 11804, "sha256": "82dae0644b5ce591c3e4af7bf9fdbfa6aeec11591560cb785ab0727a65d8eda1" }, "environment": { "id": "lean-lake-environment", "path": "/formal/evidence/current/ENVIRONMENT.json", "filename": "ENVIRONMENT.json", "bytes": 9793, "sha256": "622ce56958f1dce7e28a26615c618313dc7d62046932301cdac06880ba7000ff" }, "note": "Fresh Built modules, not Replayed. Distinct from the author evidence/build.log. Machine-checking of the selected maps; not peer review and not independent reproduction of Papers I–VII." }, "execute": { "cwd_hint": "formal", "commands": [ "python3 scripts/check_axioms.py evidence/axioms.log", "python3 scripts/check_axioms.py evidence/current/axioms.log" ], "lake_commands_run_here": [ "lake update", "lake exe cache get", "lake build", "lake env lean Omega/AxiomAudit.lean" ], "expected": "Checked 147 theorem reports; axioms: Classical.choice, Quot.sound, propext" }, "evidence_kinds": [ "lean_source", "author_transcript", "implementation_conformance" ], "source_ids": [ "paper-i", "paper-ii", "paper-iii", "paper-v", "paper-vii" ], "claims_not_made": [ "uniqueness of the measurement rule among all measurements of an unmarked outline", "additional source paper", "joining theorem", "peer review of Papers I–VII", "independent reproduction of Papers I–VII", "cubature, codec, workbook, or Machin-series route" ] }, { "id": "julia-mathematical-proof-companion", "object": "Julia mathematical proof companion v0.1", "kind": "exact_finite_certificate", "definition_paper": "paper-vii", "definition": "Companion software OmegaNaughtProofs 0.1.0: written proofs and exact executable certificates corresponding theorem-by-theorem with omega_provenance v0.1. Selected measurement G=aφ, C=aπ, W=a(φ+π), λ=G/W. Frozen SRSD remains external. Not an additional source paper.", "page": "/julia-proofs", "claim_ids": [ "julia-proof-companion" ], "package": { "name": "OmegaNaughtProofs", "version": "0.1.0", "uuid": "ce7051c8-1e3c-4a41-942b-a29bda16e583", "julia": "1.11.6", "files": 68, "source_lines": 74508, "uncompressed_bytes": 3847030 }, "artifacts": { "sha256sums": { "id": "julia-proof-sha256sums", "path": "/julia-proofs/SHA256SUMS", "filename": "SHA256SUMS", "bytes": 6301, "sha256": "716a6659ff5893f722854e13a6a97e7d30235e7f5268ad3a4e02c21cd25096f9" }, "readme": { "id": "julia-proof-readme-md", "path": "/julia-proofs/README.md", "filename": "README.md", "bytes": 6289, "sha256": "71de22038e8c4ebe9bb391d7e4b995adf4061b1494e4d075f629c73bd0746c78" }, "proofs": { "id": "julia-proof-proofs-md", "path": "/julia-proofs/PROOFS.md", "filename": "PROOFS.md", "bytes": 26771, "sha256": "a1da438398d4df276d5abd441c8baa654ff98312ece80e9211a6db05a40cd048" }, "translation": { "id": "julia-proof-translation-md", "path": "/julia-proofs/TRANSLATION.md", "filename": "TRANSLATION.md", "bytes": 9240, "sha256": "9b6c232e062806665a3223f90edad4e838988f188b36bfb95a147d39245eadb7" }, "theorem_guide": { "id": "julia-proof-theorem_guide-md", "path": "/julia-proofs/THEOREM_GUIDE.md", "filename": "THEOREM_GUIDE.md", "bytes": 89735, "sha256": "7a609115531637ecd1ef04b2b125e2f5e795875fad20b4dab1cd45ee6d966c70" }, "theorems": { "id": "julia-proof-theorems-toml", "path": "/julia-proofs/THEOREMS.toml", "filename": "THEOREMS.toml", "bytes": 89430, "sha256": "8b27cf29d5c9c738fa00eea721168ca7409ad2ce97417123e5263fdb7abc4c35" }, "reproduction": { "id": "julia-proof-reproduction-md", "path": "/julia-proofs/REPRODUCTION.md", "filename": "REPRODUCTION.md", "bytes": 8273, "sha256": "2659313e6df58b03e6a1181fd786015d02e0091ef300110cf78685a8f9a0195b" }, "run_proofs": { "id": "julia-proof-run_proofs-jl", "path": "/julia-proofs/run_proofs.jl", "filename": "run_proofs.jl", "bytes": 288, "sha256": "16a035f69fb06623d85260a9bde03d05d97bd0a0772d88636922d5cb2fe0ae1a" }, "o0_log": { "id": "julia-proof-evidence-o0-log", "path": "/julia-proofs/evidence/O0.log", "filename": "O0.log", "bytes": 1552, "sha256": "93db690c00cc4ef19270895bd5a78fd497b67a27c58f871692d03575d3564df4" }, "o3_log": { "id": "julia-proof-evidence-o3-log", "path": "/julia-proofs/evidence/O3.log", "filename": "O3.log", "bytes": 1552, "sha256": "93db690c00cc4ef19270895bd5a78fd497b67a27c58f871692d03575d3564df4" }, "word_transcription": { "id": "julia-proof-docx", "path": "/julia-proofs/downloads/OMEGA_NAUGHT_Julia_Proof_v0.1_Complete_Verbatim.docx", "filename": "OMEGA_NAUGHT_Julia_Proof_v0.1_Complete_Verbatim.docx", "bytes": 1795998, "sha256": "7df27d9efd8bc5cfab1129b598c59bf0f0f47d12b5a1f581751c3fee41616bc7" }, "reconstructed_zip": { "id": "julia-proof-reconstructed-zip", "path": "/julia-proofs/downloads/OMEGA_NAUGHT_Julia_Proof_v0.1.reconstructed-from-members.zip", "filename": "OMEGA_NAUGHT_Julia_Proof_v0.1.reconstructed-from-members.zip", "bytes": 1683196, "sha256": "b5d4e46ac32ac4ec08f96a6fc609fe8c8c3a291b7226809c2e79c3adac2e26ab" }, "inventory": { "id": "julia-proof-inventory", "path": "/julia-proofs/downloads/INVENTORY.json", "filename": "INVENTORY.json", "bytes": 15157, "sha256": "3dbce6bed7dcac0e3051c305391436af883422dbea2a7c41fdccba84b8efcb5b" } }, "author_stated_original_zip": { "filename": "Julia_OMEGA_NAUGHT_Julia_Proof_v0.1.zip", "sha256": "ef8f1eb75b83f1e5763d280374eb8b73d9ab00b8dcb76b1824aee771869cd27a", "bytes": 1681923, "path": "/extension/sources/Julia_OMEGA_NAUGHT_Julia_Proof_v0.1(1).zip", "bytes_recovered_from_word": false, "hosted_from_later_source": true, "note": "Not recovered from the Word transcription. The original container is hosted with the NS extension sources and matches SHA-256 ef8f1eb7…." }, "lean_reference": { "files": 29, "match_public_formal": true, "note": "reference/Lean/ is byte-identical to the overlapping hosted /formal/ files. Hosted Lean evidence and Julia execution records stay separately identified." }, "execute": { "cwd_hint": "julia-proofs", "commands": [ "julia --startup-file=no --project=. scripts/check_inventory.jl", "julia --startup-file=no --project=. run_proofs.jl", "julia --startup-file=no --project=. scripts/reproduce.jl", "julia --startup-file=no --project=. examples/reconstruction.jl" ], "named_runtime": "Julia 1.11.6 (author-supplied; not run on this archive)", "expected": "O0 and O3 exit 0; six identical certificate files; 147 indexed declarations; 97 polynomial zero residuals; 32768 states; 753664 transitions", "note": "Author-supplied evidence/O0 and evidence/O3 are archived transcripts. Reproduction driver updates run metadata; retain archived evidence separately. Julia is not installed on this archive." }, "julia_execution": "not_run_on_this_archive", "evidence_kinds": [ "exact_finite_certificate", "author_transcript" ], "source_ids": [ "paper-i", "paper-ii", "paper-iii", "paper-v", "paper-vii" ], "independent_of": [ "class-i-cubature" ], "claims_not_made": [ "additional source paper", "joining theorem of the eight source works", "peer review", "independent third-party reproduction", "Julia execution on this archive", "lake kernel-check", "cubature package for 10 ≤ f ≤ 21", "exact-weight/verifier payload for f = 23 and f = 24", "uniqueness among all measurements of an unmarked outline", "original ZIP container unavailable" ] }, { "id": "typed-map-audit", "object": "De-branded executable audit of typed maps", "kind": "exact_finite_certificate", "definition_paper": null, "definition": "Python/SymPy audit of maps already typed among Papers VII, V, I, II and frozen SRSD: affine contraction, floor equality on D_15, remainder-ledger reconstruction, external quotient–residual encoder, Euclidean homothety of six kernel marks. Name identification is not a joining theorem.", "page": "/network", "claim_ids": [ "typed-connection-audit", "typed-network-interfaces" ], "artifacts": { "source": { "id": "typed-connection-py", "path": "/network/typed_connection_proof.py", "filename": "typed_connection_proof.py", "bytes": 31256, "sha256": "a0c32a3c37fbf217d8111aaa8dd5cc0050d0e302df3ae339b05d99556bb32281" }, "runtime": { "id": "typed-connection-runtime", "path": "/network/typed_connection_proof.runtime.txt", "filename": "typed_connection_proof.runtime.txt", "bytes": 2397, "sha256": "1335a532ae210dccae24532e9fccf0ae3c94f5f8ec83d3e81770309ebe6633a6" } }, "execute": { "cwd_hint": "network", "commands": [ "python3 -m pip install -r requirements.txt", "python3 typed_connection_proof.py" ], "expected": "FINITE FLOOR CERTIFICATE: PASS for every integer d in [0,32767] (32768 states; q