Home › Changelog Archive changelog Site and deposit events for this archive. Frozen G6_RELEASE/1.1 bytes are not rewritten by later documentation or license corrections. 2026-09-13 Lean lake build hosted; cubature 10–21 and 23–24 still not supplied Geometry generated/ recipe, f=22 python3 -O guard, and Paper IV five-design wording are retained. lake build of hosted omega_provenance v0.1 was run on this archive on 2026-09-13 (Lean 4.19.0 commit 6caaee842e94, Lake 5.0.0-6caaee8, Mathlib v4.19.0). Fresh transcripts: evidence/current/build.log 1,960 bytes SHA-256 ddc10580… (Built, not Replayed; Build completed successfully); evidence/current/axioms.log 11,804 bytes SHA-256 82dae064… (byte-identical to the author log; 147 reports; axioms {propext, Classical.choice, Quot.sound}). Zero sorry, admit, or native_decide in hosted sources. Toolchain and .lake are not hosted. Cubature 10–21 evidence was not added: no orbit-mass files, verifiers, or transcripts were supplied, so none are hosted. Frequencies 23–24 evidence was not added: the 117 exact a+b√5 pairs, runnable verifier (cited SHA-256 41d83727…), and 109-residual ledger remain unhosted; the printed existence theorem and audit extract stay as they were. Papers remain seven. Frozen G₆ bytes unchanged. The archive is not fully fixed while those cubature packets are missing. 2026-09-13 Geometry generated/ recipe, f=22 python3 -O guard, Paper IV five-design wording Empty-folder Paper VII recipe now places published JSON and OBJ in generated/ for the unchanged verifier, hash-checks those exports, and documents independent generation into regenerated/. Frequency-22 Python verifier revision r2 (17,584 bytes, SHA-256 d9b2450e…) refuses python3 -O / -OO / PYTHONOPTIMIZE; original 16,972-byte verifier, zip f63c43e1…, and SHA256SUMS.txt 1636/f31106c5… are unchanged. Paper IV summary now distinguishes finite-grid five-designs from the limiting equal-weight measure, which differs from uniform spherical area first at degree six, matching the deposited abstract at 10.5281/zenodo.22033917. Cubature 10–21 remains unpackaged. Frequencies 23–24 keep the hosted existence theorem; the 117 exact coefficient pairs are not invented here. lake build has not been run on this archive; Lean 4 is not installed here. Papers remain seven. Frozen G₆ bytes unchanged. 2026-09-13 Software-dependency transcription; G₆ Cargo is crate-free Hosted OMEGA_NAUGHT_Software_Dependencies.docx (45,009 bytes, SHA-256 3841413f…). All eleven transcribed lock and declaration files match the hosted bytes. The G₆ and OMEGA_NAUGHT/1.0 Rust runners declare no third-party crates; the named Cargo command is cargo run --release --offline --locked and does not fetch crates. Julia companion depends only on standard libraries Dates, SHA, and TOML. Lean still records lake build as not run here. Cubature 10–21 remains unpackaged. Frequencies 23–24 keep the stated existence theorem; the 117 exact coefficient pairs are not invented here. Papers remain seven. Frozen G₆ bytes unchanged. 2026-09-12 Reproduction recipes, f=22 manifest metadata, remainder-format rejection Empty-folder recipes now match the archive layouts: Julia reconstructed ZIP extracts into OMEGA_NAUGHT_Julia_Proof_v0.1/ and is hash-checked before unzip; G₆ extracts into G6_RELEASE_1.1/g6 before julia/run.jl and cargo; frequency-22 is a flat ZIP, so SHA256SUMS.txt is not downloaded before unzip. Artifact f22-sha256sums records 1636 bytes and SHA-256 f31106c5… over 16 listed files. Reconstruction remainder overrides that are negative, fractional, or nonnumeric are remainder-format failures; remainders ≥ S are remainder-bound failures; neither reconstructs. Cubature 10–21 remains unpackaged. Frequencies 23–24 keep the stated existence theorem; the 117 exact coefficient pairs are not invented here. lake build and the archived Julia companion execution record are unchanged. Papers remain seven. Frozen G₆ bytes unchanged. 2026-09-12 Demonstration and equation corrections SRSD worked example now prints E_S(Qd)=(d′,ρ) and the normalized E_1(qd)=(d′,ρ/S) with unreduced remainder 639958766566422/10^15 for seed 399. Kernel reconstruction fetches the hosted node log, validates it, reconstructs coordinates from the hosted frame, and reports specific failures. Integrity check hashes each Julia and Lean SHA256SUMS member. Reconstruction reverse uses the displayed prefix and includes a malformed-remainder control. Remaining doubled TeX on Dynamics, Ω₀, SRSD, branches, Integration, Formal, and the Class-I degree cases is converted to String.raw. λ is described as fixed by the specified construction and selected measurement. Reproduction recipes start from an empty folder. Cubature 10–21 remains unpackaged. Frequencies 23–24 keep the stated existence theorem; the 117 exact coefficient pairs are not invented here. lake build and Julia 1.11.6 have not been run on this archive. Papers remain seven. Frozen G₆ bytes unchanged. 2026-09-12 Homepage and process revision The site now treats OMEGA as the specified marked construction. Homepage and primary navigation follow construction, selected measurements G=aφ and C=aπ, contraction, certified floor, reconstruction, proofs, and reproduction. Construct stages name Added / Determined by / Expression / Source / Why. Web labels distinguish W_readout from W_scaffold, S_mod from S_space, ρ_rem from ρ_rad, and T_map from geometric T±. Navigator covers 147 indexed statements. Archive-integrity checks the Julia and Lean SHA256SUMS and the frozen G₆ envelope. Machine source_registry resolves certificate-f22-69, certificate-f22-70, and g6-release-1-1. Cubature 10–21 remains unpackaged. Frequencies 23–24 keep the stated existence theorem; the 117 exact coefficient pairs are not invented here. lake build and Julia 1.11.6 have not been run on this archive. Papers remain seven. Frozen G₆ bytes unchanged. 2026-09-12 Julia proof companion v0.1 sources hosted Recovered all 68 original members of OMEGA NAUGHT Julia mathematical proof companion v0.1 (software 0.1.0, 74,508 source lines) from OMEGA_NAUGHT_Julia_Proof_v0.1_Complete_Verbatim.docx via FileMetadata/SourceBoundary/SourceText/SourceData styles. Hosted at /julia-proofs with SHA256SUMS match (inventory SHA-256 716a6659…). Word transcription 1,795,998 bytes, SHA-256 7df27d9e…. Author-stated original ZIP SHA-256 ef8f1eb7… is recorded; those exact container bytes were not in the Word package, so a reconstructed transport ZIP is hosted and labeled as such. All 29 Lean reference files are byte-identical to /formal/. Author-supplied Julia 1.11.6 O0/O3 logs are archived evidence, not a site run. Machine object julia-mathematical-proof-companion added. Does not supply cubature 10–21 or 23–24 payloads. Not an eighth source paper and not a joining theorem. Frozen G₆ bytes unchanged. 2026-09-12 Julia proof companion page; listed site corrections Opened /julia-proofs for OMEGA NAUGHT Julia mathematical proof companion v0.1 (software 0.1.0): written proofs and exact certificates corresponding to the 147 Lean declarations. Original package bytes from OMEGA_NAUGHT_Julia_Proof_v0.1_Complete_Verbatim.docx are not yet recovered onto this archive; hashes will be recorded only from original bytes. Author-supplied Julia 1.11.6 O0/O3 records are not a site run. Does not supply cubature 10–21 or 23–24 payloads. Not an eighth source paper and not a joining theorem. Also: typed-network floor identity typeset with \bigr\rfloor; radial-template reference is Section 10 of the hosted Python script; reduced rational 169974885672389/(5×10^14) grouped; SRSD copy says separately defined theories, not three; Lean module table no longer labels the finite certificate as kernel-checked on this archive; Open Graph and home JSON-LD use six preprints and one report, with dateModified 2026-09-12. Frozen G₆ bytes unchanged. 2026-09-12 Canonical machine contract Hosted /archive/MACHINE.json as the canonical AI-facing entry (schema OMEGA_NAUGHT_MACHINE/1.0). Ten independent objects: marked kernel, Construct transfer gate, Lean selected measurement, typed-map audit, OMEGA_NAUGHT/1.0, Class-I cubature ranges, SRSD v1.0, historical G₆, successor search, and Omega-Alpha. Each object names definition, claim ids, artifacts with hashes, evidence kind, reproduction commands, and claims_not_made. Public copies of claims, artifacts, conformance, and papers JSON sit beside it. Not a joining theorem, not an eighth source paper, not peer review, not independent third-party reproduction. lake build has not been run here. Frozen G₆ bytes unchanged. 2026-09-12 Lean 4 v0.1 sources hosted Recovered the omega_provenance v0.1 Lean sources from the Word transcription of the 29-file package. Hosted Omega.lean, thirteen Omega/*.lean modules including Metrics.lean, lakefile.lean, lean-toolchain, evidence logs, and SHA256SUMS. Every hashed file matches the package SHA256SUMS. Python 3.10.21 scripts/check_axioms.py PASS: 147 theorem reports; axioms {propext, Classical.choice, Quot.sound}. No sorry, admit, or native_decide in the hosted sources. lake build has not been run here. Author evidence/build.log is a prior transcript, not a kernel-check on this archive. Selected measurement, not uniqueness among all measurements of an unmarked outline. Not an eighth source paper, not a joining theorem, not peer review, not independent reproduction of Papers I–VII. Frozen G₆ bytes unchanged. 2026-09-11 Lean 4 geometric-provenance formalization inventory Hosted the documentation and build scripts of a Lean 4 formalization of a selected geometric-provenance measurement (Lake package omega_provenance; stated main result Omega.central_provenance_theorem). Executable .lean sources, lakefile, lean-toolchain, and evidence logs are not yet supplied, so lake build has not been run here. README claims of 147 theorems, zero sorry, and axioms {propext, Classical.choice, Quot.sound} remain author statements. Selected measurement, not uniqueness among all measurements of an unmarked outline. Not an eighth source paper, not a joining theorem, not peer review, not independent reproduction of Papers I–VII. Frozen G₆ bytes unchanged. 2026-09-09 Corrected typed-map audit source Replaced typed_connection_proof.py with the author’s corrected source (SHA-256 a0c32a3c…, 31256 bytes). Exact symbolic identities; Machin/√5/π/λ enclosures; floor equality on all 32768 states with q<λ certified; exhaustive remainder reconstruction 32768×23; seven malformed-input classes rejected. Named Python 3.10.21 / SymPy 1.14.0 runtime PASS in 13s. Geometry and Construct canvases no longer reallocate their buffers on every orbit tick. Not a joining theorem, not an eighth source paper. Frozen G₆ bytes unchanged. 2026-09-09 De-branded typed-map audit on the network page Hosted typed_connection_proof.py as an executable audit of de-branded maps already typed among Papers VII, V, I, II and frozen SRSD. SymPy symbolic identities, exact integer/rational claims, and exhaustive floor equality on D={0,...,32767} using rational enclosures of √5 and π. Homothety of the six Paper VII marks is Euclidean scaling, not a unique shell. Radial template identities in the script are algebraic and are not a physical theorem. Named Python 3.10.21 / SymPy 1.14.0 runtime PASS. Not a joining theorem, not an eighth source paper. Frozen G₆ bytes unchanged. 2026-09-06 Marked kernel explained as a typed transfer gate Geometry now states what the OMEGA shape is (a marked planar kernel, not a volume or unique shell), what is rigid in it, and how Construct mode and OMEGA_KERNEL_NODES/1.0 act as a transfer gate: kernel data may pass, the scaffold only if adopted, exclusions and 12° display coordinates do not travel. Scalar Ψ/Φ remains a side channel of numbers, not a geometric reconstruction and not a joining theorem. Frozen G₆ bytes unchanged. 2026-09-06 Kernel Construct mode on Geometry Geometry page now runs OMEGA Kernel Construct v1.1.0: a fifteen-stage presentation machine, OMEGA_KERNEL_NODES/1.0 true-ε export, and a 12° non-normative display. Adapter only; paper-vii-kernel.ts remains the evaluator. Replay stops at kernel stage 15. Adopted scaffold is a deliberate jump. Hosted technical paper, canonical node log, and exact scalar-interface Python certificate. Not a source work, not a joining theorem, not a 3D shell. Frozen G₆ bytes unchanged. 2026-09-05 Typed network dossier and f=23,24 finite-audit extract Hosted the 5 September 2026 typed-network proof dossier at /network. It types exact interfaces among Papers VII, V, I, II and frozen SRSD, and keeps the cubature branch logically independent. Not a joining theorem. Printed f=23,24 finite-audit data are extracted: free orbits, minima (21,1,1) and (23,1,0), rank witnesses, canonical weight-text hashes, and a quoted same-environment replay. The 117 exact Q(√5) masses and runnable verifier are cited as LaTeX filecontents and are not extractable from the hosted PDF. Binary64 minimum-selection is corrected in format 1.1; exact weights, identities, positivity, and rank witnesses unchanged. Frozen G₆ bytes unchanged. 2026-09-03 X₂₃ and X₂₄ positive existence theorem Locally hosted existence theorem: X₂₃ admits strictly positive H₃-invariant cubature weights exact through degree 71, and X₂₄ through degree 75. No maximality. Rank A₂₃=52 and rank A₂₄=57, each with affine dimension 4. Does not enlarge Paper VI. Hash-pinned weights, verifier, and residual ledger are not enumerated. The all-frequency conjecture is now open from f ≥ 25. Frozen G₆ bytes unchanged. 2026-09-03 Canonical archive overview Hosted scoped overview at /archive/OVERVIEW.md. Paper IV wording is the first equal-weight harmonic obstruction at degree six on the specified radial Class-I grids. Paper VII Construction-to-OMEGA summary names six baseline marks, every distance among them and from them to α, all fifteen pairwise center angles, rank-two Gram data, and an oriented frame in R³. Indexed claim records use independent axes; browser audit PASS results are dated executions, not permanent site state. Frozen G₆ bytes unchanged. 2026-09-02 Comprehensive Julia kernel, fan, Gram, and scaffold Companion Julia script now materializes the unit-scale Paper VII v1.6 object in one environment: six marks, major arc, golden feet, complete 15-pair center-angular fan, Gram factorization Ḡ=c²11ᵀ+zzᵀ, and the Definition 11.1 outer scaffold. Binary64 evaluation and numerical checks only; rank and isapprox do not prove the theorems. Foot parameter is ℓ, not λ. Oriented R³ view draws the six center rays and the scaffold. Frozen G₆ bytes unchanged. 2026-09-02 Paper VII v1.6 Zenodo preprint Paper VII is public at DOI 10.5281/zenodo.22233573 (concept DOI 10.5281/zenodo.22233572). Title: Construction-to-Curve Theorem for a One-Arcsecond Circular Seed with Bilateral Golden Extensions, version 1.6. The Construction-to-OMEGA theorem proves existence, uniqueness, exact characterization, and rigid-motion uniqueness of the marked kernel. Local v1.6 PDF, publication-ready package, v1.6 generator, JSON/OBJ exports, and verify_geometry.py are hosted. Versions 1.4, 1.2, and 1.1 remain as superseded local drafts and are served noindex, noarchive. citation_doi is now emitted. Frozen G₆ bytes unchanged. 2026-09-02 Oriented R³ kernel reconstruction Geometry page Oriented R³ view now uses the Theorem 7.1 major-arc parametrization C(t)=α+a(cos t u + sin t v) for δ≤t≤2π−δ, with golden feet L± of length aφ². Drag to orbit; scroll to zoom. Companion Julia script omega_kernel_oriented_r3.jl hosted. Frozen G₆ bytes unchanged. 2026-09-02 Paper VII v1.4 locally hosted prepublication draft OMEGA Marked Reference Geometry hosted at /papers/vii and /geometry. Version 1.4 proves constraint closure of the one-arcsecond seed: six baseline marks, complete 15-angle center fan, Gram rank two, and exact oriented realization in R³. Companion generator, JSON landmark record, and sampled OBJ are hosted. Metric outer scaffold is an adopted transcription of the notebook a, aφ annotations; remaining outer curves and signed-depth completion are not claimed. Versions 1.2 and 1.1 are superseded local drafts and are served noindex, noarchive. Related prototypes hosted separately: OMEGA_REFERENCE_GEOMETRY/0.1 state schema and OMEGA drift experiment v0.1, a falsification control that finds no universal privilege of a 4D OMEGA anchor. Frozen G₆ bytes unchanged. 2026-09-02 Paper VII v1.2 locally hosted prepublication draft OMEGA Marked Reference Geometry hosted at /papers/vii and /geometry. Local rigidity of K_Ω(1), declared golden-ratio extensions, center-relative reconstruction, and positive-homothety scaling. Outer Space/Echo/Loco completion is not claimed. DOI 10.5281/zenodo.22233573 reserved; Zenodo record not yet public. No citation_doi is emitted. Version 1.1 is a superseded local draft and is served noindex, noarchive. Frozen G₆ bytes unchanged. 2026-08-30 Naming and vocabulary Homepage section above the epistemic layers: project-specific names identify author-defined constructions and do not claim invention of standard operations, privilege, priority, or general adoption. Standard glosses for SRSD, Newman’s Omega map, Omega/JPRV, and Ω₀ = φ + π. 2026-08-30 Standard-mathematics and claim-scope notice The primitive SRSD encoder and decoder are identified as standard coordinatewise quotient–residual decomposition. SRSD does not claim to invent division with remainder or to provide a new foundation for mathematics. Foundational closure means internal sufficiency of frozen SRSD v1.0. The archive makes no blanket claim of novelty, priority, peer review, or independent validation. 2026-08-30 Training module v2.1.0 and global-object PDF noindex Current AI training download is OMEGA_JPRV_SRSD_CANONICAL_TRAINING_MODULE_v2.1.0, aligned to SRSD as a frozen external audit instrument. v2.0.0 is retained as an immutable historical artifact and served noindex, noarchive. The Global Mathematical Object Papers I–V PDF keeps its bytes and is served noindex, noarchive. Navigation label is Audits. Frozen G₆ bytes unchanged. 2026-08-30 Frozen SRSD header figure The homepage header now carries the Frozen SRSD lossless-resolution figure in ℝ³. The same figure leads the SRSD instrument page. Encoder/decoder identities in the caption are unchanged: E_s(y)=(d,ρ), y=Δ_s d+ρ, 0≤ρ_i<s_i. 2026-08-30 SRSD external-audit architecture G₆ is labeled historical/superseded integration packaging. SRSD v1.0 is the frozen external audit instrument, not the foundation of a combined object. Independent audits report without a global aggregate. Raw G₆ specification pages are noindexed. Frozen G6_RELEASE/1.1 and 1.2 bytes are unchanged. Frequency-22 wording now says Python and Julia pass separately. 2026-08-28 PDF canonical headers and scholarly identity metadata Local Paper I and Paper VI PDFs send Link rel=canonical to their Zenodo files. Superseded f22 PDF sends X-Robots-Tag: noindex, noarchive. ORCID author link, rel=me identity links, f22 bibliographic title, and G6 1.1 sitemap lastmod added. Frozen G₆ bytes unchanged. 2026-08-28 Version metadata and frequency-22 supplement relation Social description uses five mathematical preprints and one Zenodo report. JSON-LD carries document and Zenodo deposit versions. Frequency-22 structured metadata records IsSupplementTo 10.5281/zenodo.22068873 without enlarging the Paper VI theorem range. Frozen G₆ bytes unchanged. 2026-08-28 Paper I concept DOI, 404 page, and citation surfaces Live G₆ specification carries a Paper I DOI erratum without mutating frozen 1.1/1.2 bytes. Artifacts, 404, social metadata, Paper VI citation PDF, and footer license wording updated. 2026-08-28 Paper I concept DOI Primary identifier is the working concept DOI 10.5281/zenodo.21830284. Version v1 remains Zenodo record 21830285. The version-specific DOI resolver is marked unavailable; the site does not depend on it. 2026-08-28 Scholarly metadata and archive navigation Page-specific Open Graph titles; Paper V represented as a Zenodo report; exact ISO publication dates; unique citation PDF URLs; /artifacts index; site changelog; report page linked from every footer. G₆ 1.1 bytes unchanged. 2026-08-28 Paper III title and homepage purpose Paper III title aligned to the Zenodo record. Homepage states the archive purpose in one sentence and a five-row status snapshot. 2026-08-27 Frequency-22 correction v1.1 Minimum positive degree-69 orbit corrected to (11, 11, 0) by exact comparison in ℚ(√5). Canonical solution digests unchanged. Python 3.12.13 and Julia 1.11.6 both CERTIFICATE PASS. Addendum PDF v1.0 superseded and noindexed. 2026-08-28 G6_RELEASE/1.2 license-and-documentation correction Docs/data CC BY 4.0; source MIT. Canonical record SHA-256 92187a21… unchanged. Frozen G6_RELEASE/1.1 retained. Envelope SHA-256 0235d461…. 2026-08-23 Paper VI document version 1.3 Exact positive cubature on 1 ≤ f ≤ 9. Local PDF hosted. Zenodo deposit version 1 is a different version axis from document version 1.3. 2026-08-23 G6_RELEASE/1.1 frozen Computational envelope frozen. Canonical record SHA-256 92187a21…. cubature_frequency_max=9. External archival pending. 2026-08-21 Paper V Zenodo report OMEGA NAUGHT Ω₀ deposited as a Zenodo report. Not a preprint and not peer reviewed. 2026-08-20 Paper IV Zenodo preprint Radial icosahedral sampling and first harmonic obstruction deposited as Zenodo record 22033917 (deposit v1). 2026-08-14 Paper III Zenodo preprint SRSD foundational closure specification version 1.0 deposited as Zenodo record 21927248. 2026-08-09 Paper II Zenodo preprint Ordered Euclidean remainders deposited as Zenodo record 21843485 (deposit v1). The PDF filename revision label v2 is not a separate deposit. 2026-08-07 Paper I Zenodo preprint Quantized Omega contraction theorem deposited as Zenodo record 21830285 (version v1). Concept DOI 10.5281/zenodo.21830284.
