Archive changelog
Site and deposit events for this archive. Frozen G6_RELEASE/1.1 bytes are not rewritten by later documentation or license corrections.
2026-10-27
600-cell signal network, unpublished reserved DOI
Added pages for a declared 120-signal extension on the 600-cell graph, its modulo-8 witness, the network coefficient interval, and reproduction records. The typed interface network is unchanged. The author-reported DOI 10.5281/zenodo.23688676 stays unpublished and is not a ninth source work. The parameter audit was rerun here on Python 3.10.21; its JSON matches the stored assessment file. The 26 October joint-witness stdout remains a historical Python 3.12.14 record. SciPy is not installed for this site run. A positive-simplex corollary is labeled as a written real-arithmetic derivation and is not a six-mark test. Written arguments were not reviewed as proofs. A matching digest checks byte integrity. It does not itself verify that the recorded execution occurred or that the checker is mathematically correct.
2026-10-24
Corrected scaling statement, restored proofs, and a site run of the reference checker
Replaced the finite-step contraction sentence. Exact scaling by a nonzero lambda is injective; integer quantization, not that scaling, is what has multiple predecessors. Restored the reference checker, PROOFS.md, and the v2 unification document from embedded attachments whose SHA-256 values match the printed manifest. The 18-page reference PDF was not in that file and is not hosted. This archive ran the restored checker on Python 3.10.21, normal and optimized: both exited 0, stdout matched, stderr empty, 19 groups. The Decimal/DFT group is numerical. The conversation record remains Python 3.12.14, and its stdout differs in that version line. Written arguments were not reviewed as proofs. The working decoder and the earlier Python/Java records were kept. Frozen G6 and the eight counted source works were not changed. A matching digest checks byte integrity. It does not itself verify that the recorded execution occurred or that the checker is mathematically correct.
2026-10-24
Compatibility note, reference language, and a site run of the v2 checkers
Added supplementary reading for geometric arithmetic compatibility, reference recovery, and OMEGA-LANGUAGE 0.1, plus a decoder. The Python and Java v2 sources match the printed digests and were run here on Python 3.10.21 and OpenJDK 17.0.20: four exits 0, identical stdout. The conversation record remains Python 3.12.14. The reference checker source and its PDF were not recovered as the named bytes, so they were not given a site PASS. Written arguments were not reviewed as proofs. Frozen G6, Paper VII, and the eight counted source works were not changed. A matching digest checks byte integrity. It does not itself verify that the recorded execution occurred or that the checker is mathematically correct.
2026-10-24
Share card and feed banner
Replaced the link-preview image and the wide feed banner. Both show the existing marked construction and the title OMEGA NAUGHT. The site is not marked as a game. The previous card remains at /images/omega-layout-v1/omega-share.png.
2026-10-23
Homepage research identity
Clarified the homepage research identity and aligned its metadata and structured data. Mathematical content, archived artifacts, and existing evidence statuses were not changed.
2026-10-15
Supplement 1 workflows
Added canonical six-mark readouts, a witness lab for rank-losing integer layers, and an exact degree-at-most-2 transfer between three rotations of the twelve-node rule. verify_supplement_1.py is 25,845 bytes, SHA-256 09d2fa0e6b5ac34a50344177c67aa4a3b0159565c8ac3aeccf728db4437c51e3. This archive ran it on Python 3.10.21: exit 0 in both modes, logs byte-identical. The sine is named and is not evaluated. The cyclotomic degree formula is cited, not reproved. Witness records are 77 bytes; that length is not an optimality claim. Higher subdivision frequencies are not enabled. Frame calibration, boundary-field targets, and Lean or SMT generation are not in this release. Formal execution was not run. The 15 October thesis file and frozen G₆ are unchanged. A matching digest checks byte integrity. It does not itself verify that the recorded execution occurred or that the checker is mathematically correct.
2026-10-15
Relative representation thesis hosted
Hosted the 15 October 2026 thesis at /geometry/relative-representation. The written arguments have not been reviewed as a proof. The cover disclaims independent peer review, a proof-assistant kernel, physical unification, and a mathematical proof of the divine. The companion source was not attached. verify_omega_thesis.py is a transcription of the printed Appendix B listing, 18,211 bytes, SHA-256 e6330f8327f3ce39c61ca666864171a3470044117147b20a3237ba1931e7d506. This archive ran it on Python 3.10.21: exit 0 in both modes, logs byte-identical, 28 free-variable identities, and a finite audit of 32,768 seeds at horizon 23. The thesis’s Python 3.13.5 logs were not supplied. The auxiliary seed 1/2 is not the canonical sine. A matching digest checks byte integrity. It does not itself verify that the recorded execution occurred or that the checker is mathematically correct. Not an amendment of Paper VII. Frozen G₆ unchanged.
2026-10-15
Integration proof bundle hosted
Hosted the 14 October 2026 integration ledger at /geometry/integration-proofs. It states 34 theorem records and 12 excluded claims. This archive has not reviewed those written arguments as a proof. The certificate file is 1,722,817 bytes, SHA-256 daaee23b3c27bbb320d0f8db2c8d00a4a077f08e5fe0056864323873ddf71b19. This archive reran verify.py on Python 3.10.21: exit 0 in both modes, 2,314 algebra checks, and a finite audit of 32,768 seeds at horizon 23. The logs match the supplied Python 3.13.5 report except the runtime string. Julia, Rust, the adversarial script, and the SymPy script were not in this upload and were not run. A matching digest checks byte integrity. It does not itself verify that the recorded execution occurred or that the checker is mathematically correct. Not an amendment of Paper VII. Frozen G₆ unchanged.
2026-10-13
Core recovery note hosted
Hosted the 13 October 2026 note at /geometry/core-theorem. The note states five conclusions and written arguments for them. This archive has not reviewed those arguments as a proof. The checker is 16,815 bytes, SHA-256 e044133aceefb442bfa226bdf61359a58bca413e12196f090ff19eef3ef84ab5, the same bytes named in the supplied Python 3.12.14 record. This archive reran both commands on Python 3.10.21: exit 0, logs byte-identical and matching the supplied transcript body. The finite audit is 32,768 states at horizon 23. It does not enumerate every integer below 42,189,065. A matching digest checks byte integrity. It does not itself verify that the recorded execution occurred or that the checker is mathematically correct. Not an amendment of Paper VII. Frozen G₆ unchanged.
2026-10-11
Transition checker described in two parts
The transition page now separates the free-variable identities from the finite ledger audit. The symbolic checks are identities under the stated assumptions. The 753,664 checks cover seeds 0 through 32767 and horizons 1 through 23. Both executions reproduce the declared checks. Neither establishes physical unification or independent mathematical review. The shared SHA-256 identifies the same source bytes. Matching pass lines supports execution agreement. The hosted logs have recorded SHA-256 digests. Matching those digests checks byte integrity. A matching hash does not itself verify that the recorded execution occurred or that the checker is mathematically correct. Frozen G₆ unchanged.
2026-10-11
Transition invariant checker
Hosted the transition-invariant checker at /geometry/transition-invariants. The source is 12,112 bytes, SHA-256 e94400b6e136bed009388c5d17e4f1c698235b7b938f75c266bbaf363a15a0ca, the same bytes named in the supplied Python 3.12.14 record. This archive ran both commands on Python 3.10.21: exit 0, eight groups, 753,664 prefix invariants, longest extinction step 10. The canonical sine is not evaluated. This is not a Lean certificate, an independent review, a physical experiment, or a unification proof. Frozen G₆ unchanged.
2026-10-08
Six-mark sampling polar
Hosted a derived note at /geometry/sampling-polar. For s>0 the normalized marks give an invertible sampler on polynomials of degree at most five. The added sample bound defines a polar pair with volume product 256/45. This-archive Python 3.10.21 ran Appendix A on 8 October 2026: four exact lines, exit 0 under python3 and python3 -O. Those checks use rational seeds in Q(phi), not the canonical sine seed. The two-ball packing remains conditional on A-087 and A-343, which were not executed. Not a source paper and not an amendment of Paper VII. Frozen G₆ unchanged.
2026-10-08
Construction figures on the pages
The home page, the geometry page, and the ellipse note now show figures drawn from the scale-one formulas: the marked plan, the equal-weight moment ellipse, and the outer-scaffold rectangle. The hosted notebook diagram and frame photograph are displayed on the geometry page. They were already in the file archive and were not previously shown. R is not φ. Frozen G₆ unchanged.
2026-10-08
Verification labels corrected
The 7 October report paired implementation passes with NOT_RUN and marked every claim NOT_FORMALIZED. Both pairings are withdrawn. The committed registry at e5b4edc has 49 claims and 37 implementation passes. Current counts are generated from the registry, not copied into this sentence as a live total. A recorded pass now says that the historical execution was not repeated, unless this audit actually ran it. The general floor checker was repeated on 2026-10-08; the 7 October log remains. Ledger.lean already states the integer division identity; that source was read and not rebuilt. Unexamined claims are NOT_ASSESSED, which is not a claim that no formalization exists. The ellipse note's SRSD status names that note only. No conformance, language, or independent-review award was added. Frozen G₆ unchanged.
2026-10-07
Verification axes and the general floor step
Claim records now carry separate SRSD, written-review, formal, computational, and language axes. Those axes do not reclassify older conformance passes. ASD-STE100 Issue 9 remains SOURCE_UNAVAILABLE, so no language conformance is awarded. A filled Part 14 template cannot be labeled SRSD-conformant. The general integer floor step is claim floor-transition-general: this-archive Python 3.10.21 ran 290 explicit checks, exit 0 under python3 and python3 -O. That pass is not a proof review, not a Lean check, and not a verification of the archive. The 399 statement was not revised. The ellipse note has registry id operator-bridge-note and was not reviewed. Frozen G₆ unchanged.
2026-10-07
Ellipse and operator bridge
Hosted a derived note at /geometry/operator-bridge. Equal-weight second moments of the six center-relative landmarks define a filled ellipse; an affine chart recovers source angles with a target metric; a two-by-two operator has that ellipse as its numerical range. The arc-and-feet curve is not the ellipse, and R is not φ. Supplied Python 3.13.5 / NumPy 2.3.5 / SymPy 1.14.0 record: 23 groups PASS in normal and optimized modes. This archive did not rerun it. Julia source matches SHA-256 9f81f385… and was not executed. Not a source paper, not peer review, and not an amendment of Paper VII. Frozen G₆ unchanged.
2026-10-01
Canonical marked spatial view
The identity-pose kernel is now drawable. Front looks along n. The edge along x collapses the planar kernel, and the six marks overlap. One oblique camera is offered as a chosen orientation, not a second curve. Selected paths highlight G = aφ and C = aπ. The Space, Echo, Loco rectangle is optional and adopted. The one-arcsecond opening is a separate unequal-axis chart and is not closed by a segment. Display strokes have no thickness. This is not the proposed tangent-joined profile. Frozen release bytes are unchanged.
2026-10-01
Kernel views, thickness, and revolution
Qualified the marked-kernel account. A view along n shows the outline; a view along v or u collapses it to a stated segment. Exact identities stay separate from binary64 agreement with the seven kernel nodes. Thickening, sweeping, extrusion, and revolution need extra rules. Revolving the identity-pose kernel about the y-axis merges the feet even as a point section. No thickness or depth was added. Frozen release bytes are unchanged.
2026-10-01
Spatial reference, version 1
Added a reconstructible circular, tangent-joined profile as a proposed spatial reference. Illustrative dimensions are display choices, not the archive’s marked geometry. Joins, center separation, and major-crown span are checked in floating point for three parameter cases. The page draws four construction modes and three views. No stress or electromagnetic field is solved, and the profile is not identified with the six-mark construction or with C = aπ.
2026-10-01
Tolerance names and historical TGA 2.0 links
Clarified TGA’s numerical tolerance documentation by giving gap comparisons and parameter-boundary classification distinct names. Corrected historical TGA 2.0 links to point to the frozen version 2.0 release download. The numerical implementation and frozen release artifacts are unchanged.
2026-10-01
TGA 2.1 scaling and membership
TGA 2.1 is a supplementary release. The active page counts admitted relationships from the loaded graph: 32 edges in seven relation categories, including the frozen 19 TGA 2.0 edges. Publication status, mathematical justification, execution results, and numerical comparisons stay separate sentences. Path certificates cover only the implemented schemas for Sβ∘Mr = Pr∘Sβ and F∘Mr = Dr∘F. Six-mark membership is a different type from a valid positive probability vector; uniform probabilities remain valid data and are not the positive-scale family. Binary64 agreement is not an exact certificate. TGA 2.0 files and hashes are unchanged. Not a source paper and not a general theorem prover.
2026-09-27
Marked construction layout
The homepage now leads with the marked construction, six primary links, and the four calculators. TGA lists all 19 admitted relationships in an expandable index; proposals stay separate. Papers reach the eight source works before the longer scope notes. The sharing card is /images/omega-layout-v1/omega-share.png (SHA-256 5445b802…). Existing source-work count and frozen evidence remain unchanged.
2026-09-27
TGA 2.0, mathematical atlas, and build identity
Added TGA 2.0, a supplementary typed witness graph with 19 admitted relationships and seven relation categories. Exact certificates, declarations, trusted analytic schemas and information-loss witnesses are separately labeled. Published the interactive mathematical atlas and a checksummed TGA download container. Build metadata now identifies inventoried source bytes and distinguishes verified, provider-declared and unavailable Git revisions. Existing source-work count and frozen evidence remain unchanged.
2026-09-26
Numerical-range checks
Quaternion normalization now scales by the largest absolute component before the norm, so 1e200 and 1e-200 times the identity quaternion match the unit rotation. Radius 1e308 does not produce a kernel export; nonfinite numbers are rejected before JSON serialization. The boundary probe must satisfy x² + y² ≤ 8/9 on z = 1/3. Thirteen ones with probe x = 1e308 export reconstruction null and a probe-domain error, not a reconstruction value of null. Learn’s certificate glossary and the sphere degree-20 sentence were corrected. Published /workbench/releases/omega-workbench-impl-2026-09-25-r3.zip (25806 bytes, SHA-256 ddca5249…). Extracted outside the repository at 2026-09-26T00:56:45Z, Node v22.23.2 ran node scripts/workbench-recheck.mjs and exited 0. Transcript SHA-256 c18af618…. The r2 ZIP 939e4bab… and the 20:31:42Z ZIP ed1f447b… are unchanged. Not a theorem checker and not a new source paper.
2026-09-25
Typechecked workbench recheck
Typecheck: npm run typecheck (tsc --noEmit) exits 0 with no diagnostics. The annotations are in the current source; frozen evidence bytes are unchanged. Sphere editor: total degree 20 is accepted (x^20 average 1/21, no DEGREE_LIMIT). Total degree 21 is the first rejected degree (DEGREE_LIMIT, no average). An earlier “degree-20 errors” note meant an exponent of 21, not a rejection of degree 20. Published /workbench/releases/omega-workbench-impl-2026-09-25-r2.zip (22530 bytes, SHA-256 939e4bab…). Extracted outside the repository at 2026-09-25T21:53:13Z, Node v22.23.2 ran node scripts/workbench-recheck.mjs and exited 0. Transcript SHA-256 e1395d84…. The 20:31:42Z ZIP ed1f447b… stays as the pre-annotation snapshot; its checksums are not rewritten. The historical script /workbench/workbench-recheck.mjs stays SHA-256 5ec7f9c9…. Its download page points at the runnable ZIP. Implementation validation, not a theorem checker and not a new source paper.
2026-09-25
Standalone workbench recheck and tool repairs
Published /workbench/releases/omega-workbench-impl-2026-09-25.zip (22027 bytes, SHA-256 ed1f447b…). Extracted outside the repository, Node v22.23.2 ran node scripts/workbench-recheck.mjs and exited 0. Transcript SHA-256 6a19d26b…. This is implementation validation of the source at that run. It does not reproduce the 23 September source hashes; /workbench/repair-acceptance.txt stays historical. The constructor SVG export is namespaced XML. Recovery text no longer says the seed was not cleared when the textbox was emptied by hand. The magnified seed inset separates the d and b labels. Floor-kernel HTML captures are labeled historical. Export buttons stay disabled while radius, center, or quaternion input is invalid. Not a new source paper.
2026-09-25
Exact field interface corrections
The coefficient order is the displayed basis order recorded in basis_order and the checker BITS tuple, not a binary count. The seven quadratic subfield labels are square-free radicands, not discriminants. coefficient_record.schema.json is now a JSON Schema that rejects a bad count, a malformed integer string, and a zero denominator. The checker also rejects an unreduced fraction and any zero other than 0/1. python3 and python3 -O both print TOTAL 29 PASS.
2026-09-25
Exact field interface
A supplementary note at /geometry/exact-interface records the golden field inside Q(sqrt(2), sqrt(3), sqrt(5)), the eight-coefficient record, the relation between the two norms, one rational reflection, and the split between injective samples and encoded records. The first hosted checker printed TOTAL 22 PASS under python3 and python3 -O. It is not an additional source paper, does not place pi in K, and does not enlarge Paper VI, Paper VII, or paper 8.
2026-09-24
Page-specific share cards
Server-rendered HTML now sets og:title, og:description, og:url, and the matching Twitter title and description from each route’s title, description, and canonical URL. The site-wide card no longer replaces those tags. A broken changelog entry that returned HTTP 500 was repaired in the same pass. Raw HTML was checked for /dynamics/floor-kernel, /geometry/boundary-reconstruction/ten-sample, and /papers/8.
2026-09-24
Usability fixes and generated indexes
Clearing the 399 generator no longer raises SEED_REQUIRED. An empty seed reports that error only when a forward action is requested. Boundary import messages now come from the parsed token list: a bad token names its position, and a wrong length names the actual count. The beta slider follows the number field, including values outside −6 to 6. Search normalizes spaces, hyphens, and symbols, and the query is kept in the URL. The sitemap is generated from src/data/site-routes.json and src/data/site-documents.json. /notes/languages and /papers/viii redirect with HTTP 301. MACHINE.json now records buildGeneratedAt separately from contentUpdatedAt. Homepage content date is 2026-09-23.
2026-09-24
Floor-kernel downloads
The evidence directory URL now opens a file index at /dynamics/floor-kernel/evidence. The host does not list directories, so the previous link returned 404. The bundled download is /dynamics/floor-kernel/OMEGA_399_Exact_Rule_and_Grok_Handoff.zip, 87011 bytes, SHA-256 e79787b7fbb0be86b5b1bb0fd4677fe7dc8c82172f8e392c99ccb1cf1d80af07. It was assembled here from the hosted checksummed files plus SHA256SUMS.txt. It is not a recovered author ZIP. The original container was not in the upload.
2026-09-24
Exact rule beside the 399 ledger
The recover tool and the 399 walkthrough show Q = 339949771344778, S = 1000000000000000, the floor and inverse, and the 399 product before the orbit table. The note and reference checkers are hosted at /dynamics/floor-kernel. This archive ran Python 3.10.21 and Node v22.23.2 at 2026-09-24T00:50:51Z: 32768 seeds, 300871 transitions, depth 10. The site-reference runs match the supplied transcripts. The two LICENSE-CODE copies were taken from the already hosted site license because that hash is the checksummed value. No ZIP was supplied. This is not a new theorem and not a source paper.
2026-09-24
Ten-sample written note hosted
Hosted Ten_Sample_Reconstruction.md at /geometry/boundary-reconstruction/ten-sample/Ten_Sample_Reconstruction.md. 9973 bytes, SHA-256 967bc8afe442d6b0763f5d563b993a368161243d0f23b7274be46936d81639fe. The checker and both supplied transcripts are unchanged. The page renders that note. This remains a supplementary mathematical note, not an additional source paper and not a DOI.
2026-09-23
Explicit ten-sample reconstruction
Hosted the supplementary ten-sample decoder at /geometry/boundary-reconstruction/ten-sample. The checker verify_ten_sample.py is 12288 bytes, SHA-256 cc850bda…. Supplied verification.txt and verification_optimized.txt are byte-identical, 1186 bytes, SHA-256 a6e04971…. This archive replayed both commands on Python 3.10.21 at 2026-09-23T23:53:35Z; both exited 0 and matched that transcript. The author record names Python 3.12.14. The canonical Ten_Sample_Reconstruction.md, 9973 bytes, SHA-256 967bc8af…, had not yet been attached to that update. The later entry hosts it. Not an additional source paper.
2026-09-23
Homepage hook
The homepage pitch and its description now open with “Maps of Vectors included.” This is a navigation hook. It does not add a source paper or a new theorem.
2026-09-23
Imported field coefficient and fitted geometry frames
Recovered β is now the extra sample minus the quadratic value reconstructed from the same twelve measurements, divided by J at the additional point. Thirteen zeros recover β 0. The field export separates generator_reference from reconstruction, and an invalid sample exports no reconstruction. Constructor, recovered-record, and orbit drawings fit the view to the posed arc, both feet, and the six marks, including radius 3.99 and a center translated to (10,0,0). Node v22.23.2 check: node scripts/workbench-recheck.mjs, transcript /workbench/repair-acceptance.txt. Not a browser session and not a new source paper.
2026-09-23
Workbench repair after live review
Corrected the sphere tool so a zero denominator, a blank exponent, an incomplete coefficient, degree above 20, or more than 100 terms produces an input error and no average. The ledger seed field now rejects noncanonical and 101-digit text without leaving the page. Recovered records show the orbit, exact scales, pose, and marked shape, and the cleared-seed sentence is tied to that action. The constructor keeps canonical coordinates separate from the 12° schematic, rejects a nonpositive radius, and exports center and quaternion pose. The boundary tool shows the transported slice, a movable probe, imported-sample residual, recovered beta, node selection, and a field-record export. An imported twelve-value list does not borrow the generator’s extra sample. The reproduce summary now matches the 2026-09-13 lake build recorded on /formal. Node 22.23.2 acceptance transcript: /workbench/repair-acceptance.txt. This is a site repair, not a new source paper.
2026-09-22
Boundary-reconstruction checker r2 and provenance repair
Repaired the boundary-reconstruction checker’s vacuous J² spherical-moment test with an exact rational integration of the expanded polynomial. Both normal and optimized executions pass; negative controls now reject an incorrect moment and an altered coefficient. Corrected the supplementary note’s machine provenance and evidence classification, restored the transported even mode in the machine-readable kernel formula, expanded the supplementary proofs, and added the implementation run to status and conformance records. Original PDF and TeX identities are unchanged.
2026-09-21
Boundary reconstruction note hosted
Hosted the 21 September 2026 proof at /geometry/boundary-reconstruction: PDF 344230 bytes SHA-256 a8c9e39e… (unmodified); TeX with one restored leading backslash fcaadf4b…; REMARKS.md for Ψ²=Φ_{τ², 2 log φ}, the 160/60 antipodal nine-node count, and the mixed surviving kernel. This-archive Python 3.10.21 / NumPy 2.2.6: TOTAL 30 PASS. Reconstruction restricted to H_A ⊕ ℝJ. Not a source paper, not a 13-point degree-six cubature, not an enlargement of Paper VI or /extension. Frozen G₆ unchanged.
2026-09-20
Sampling-extension author evidence transcripts hosted
Hash-matched author evidence under /geometry/sampling-extension/evidence: Python, Java, and Rust stdout (7ef550cb…), rust-build stderr, cargo and Java version files. This-archive Python 3.10.21 / OpenJDK 17.0.20 reconfirmed TOTAL 21 PASS against expected.txt. Still missing: verify.jl, Rust crate and vendor, RUNTIME_SOURCES.tsv, version-julia.stdout.txt, version-rust.stdout.txt. Not a four-language this-archive completion. Not a source paper.
2026-09-20
Sampling-extension note hosted (Python/Java replay)
Hosted PROOFS.md (99d6b58e…) with verify.py and Verify.java. This-archive Python 3.10.21 and OpenJDK 17.0.20: four executions byte-identical to expected.txt, TOTAL 21 PASS. Julia, Rust vendor tree, and RUNTIME_SOURCES.tsv were not in the upload and were not reconstructed. Not a source paper. Canonical seed remains one arcsecond.
2026-09-20
Exploration 02 decoder guards and restored notation
Hosted spec-applied exploration 02 checker (15581 bytes SHA-256 4c1b3cfa…) and restored note (20104 bytes SHA-256 12f3106a…). This-archive Python 3.10.21 / SymPy 1.14.0: 21 check groups PASS, including malformed-input rejection. Named author replacement hashes 6c35365d… (15034 bytes) and e50f3443… (19434 bytes) were not in the upload, so public downloads do not match those two hashes. Canonical seed remains one arcsecond. Not a source paper.
2026-09-20
OMEGA pair-dynamics lab hosted
Interactive view of the experimental 4D pair R(2πλ)⊕R(2πμ) at /geometry/pair-dynamics. Hypothesis layer used by the drift control; not a Paper VII theorem; not a universal anchor. Recorded E4 numbers are displayed, not rerun.
2026-09-20
OMEGA object exploration 02 hosted
Hosted additional six-mark consequences at /geometry/exploration-02: note 20222 bytes SHA-256 811279cd… (attached as text.txt) and OMEGA_Object_Exploration_02.py 12390 bytes SHA-256 45f52a21…. This-archive Python 3.10.21 / SymPy 1.14.0: 19 check groups PASS. Canonical seed remains one arcsecond; the 36-degree Gauss–Lobatto member is a related family instance. Not a source paper, not peer review, not a camera-noise model. Does not enlarge Paper VII or paper 8. Frozen G₆ unchanged. Prior-run exploration_results.json was not attached.
2026-09-19
paper 8 Proof Audit 01 hosted
Hosted the 19 September 2026 localized-flow audit under /papers/8/audit-01. Hash-matched: proof PDF 306508 bytes SHA-256 e3985cb5…; audit Markdown 21406 bytes SHA-256 4617fd3f…; independent_checks.py 9339 bytes SHA-256 380c32bd…. This-archive Python 3.10.21 / SymPy 1.14.0: 29 check groups PASS, distinct from the supplied 3.12.14 results. OMEGA_Localized_Flow_Complete_Proof.tex and original independent_checks.log were not supplied and were not reconstructed. Additional work, not a relabeling of the adversarial review, not peer review, not an additional source paper, not a blowup theorem. Frozen G₆ unchanged.
2026-09-19
Paper VII Zenodo date, remaining ordinal wording, paper 8 machine cwd
Primary Paper VII publication date is now the Zenodo publication-date field 2026-09-01; manuscript cover and record-creation remain 2026-09-02. Remaining current “eighth paper” wording is “not an additional source paper.” MACHINE paper-8 execute cwd is OMEGA_Paper_VIII/companion after unzip. Frozen G₆ unchanged.
2026-09-19
Site-review corrections F1–F8
Website-summary corrections from the 19 September 2026 public-site review: Φ_{c,η} scales N by c² and preserves J; marked x-coordinates include a or are labeled x/a; fibers reciprocal is r=S/Q; extension auditor commands quote filenames with parentheses; paper 8 added to BibTeX, CITATION.cff, llms.txt, status table, and MACHINE objects; current counts use eight works and “not an additional source paper”; original Julia ZIP linked at /extension/sources/ (ef8f1eb7…); Paper VII Zenodo publication-date 2026-09-01 distinguished from manuscript cover 2026-09-02; Omega-Alpha seven-work sentence labeled retrospective. Frozen G₆ and published certificates unchanged.
2026-09-19
Paper V is the report; Paper VII is a preprint
The publication banner now classifies Paper V (OMEGA NAUGHT Ω₀) as the Zenodo report and Paper VII as preprint version 1.6. The eight-work count is unchanged: seven preprints and one report. Individual paper listings were already correct. Frozen G₆ unchanged.
2026-09-19
Publication count and paper 8 ZIP version wording
Publication banner now reads seven Zenodo preprints and one Zenodo report, counting paper 8. The hosted companion ZIP cbdf7a29… is identified as the corrected Zenodo release; 5e47b7d5… is the original submitted archive recorded in the review, an explained version difference rather than a corrupted upload. Internal manifests pass (103 top-level, 74 companion). Frozen G₆ unchanged.
2026-09-19
Accurate charts page for exact series and 3D projections
Added /charts: exact first-hitting layer counts, BigInt floor images T(n), twelve-node even moments with the degree-six obstruction −1/105, and closed-form deformation eigenvalues in dimensions 3, 4, 5, and 8. Pixel placement is binary64 display. Not a theorem, not the paper 8 HTML explorer, not a volumetric rendering of R^m.
2026-09-19
paper 8 Zenodo record retrieved; companion ZIP hosted and replayed
DOI 10.5281/zenodo.22848213 now resolves (record created 2026-09-19T18:31:24Z). Zenodo PDF matches hosted PDF SHA-256 9827d625…. Companion ZIP 1,323,852 bytes, SHA-256 cbdf7a29…, does not match review listed archive hash 5e47b7d5…. Internal SHA256SUMS matched. Checker dbf0650c… and certificate 32bcc2fe… replayed PASS on Python 3.10.21 (32768 rows, 300871 transitions, 56 monomials). NumPy 2.2.6, not pinned 2.3.5. Not peer review. Not independent third-party reproduction. Not a Navier–Stokes blowup theorem. Frozen G₆ unchanged.
2026-09-19
paper 8 manuscript hosted; companion ZIP not supplied
Hosted Exact Arithmetic Certification of Geometric Reconstruction and Transport as paper 8 (Arabic numeral; manuscript heading Paper VIII). Received PDF 286,306 bytes, SHA-256 9827d625… (35 pages); Word 72,636 bytes, SHA-256 cd009648…; adversarial review 119,042 bytes, SHA-256 1ddb7ef6…. Those PDF/Word digests do not match the review’s listed input hashes. Author-supplied DOI 10.5281/zenodo.22848213 returned HTTP 404 from Zenodo on this archive. OMEGA_Paper_VIII_Source_and_Code.zip was not supplied; companion checkers were not run. Not peer review. Not a Navier–Stokes blowup theorem. Does not enlarge Paper VI. Frozen G₆ unchanged.
2026-09-19
Reserved source work labeled paper 8, not Paper VIII
The forthcoming source-work landing is /papers/8. The label is paper 8 on purpose, without Roman numerals. /papers/viii redirects there. No PDF, DOI, or claims invented. Papers I–VII remain the deposited source works. Frozen G₆ unchanged.
2026-09-19
Paper VIII landing reserved; source files not yet supplied
Added /papers/viii as a forthcoming source-work slot. No title, PDF, DOI, hash, or claim is invented. Deposited source works remain Papers I–VII. Lean, Julia, the Navier–Stokes extension, and the fiber handoff are not Paper VIII. Frozen G₆ unchanged.
2026-09-19
Notes page reduced to a blank shell
Replaced the history-of-computer-languages notebook with a single blank Notes page at /notes (markdown twin /notes/notes.md). /notes/languages now redirects there. Not a source paper and not MACHINE evidence. Papers remain seven. Frozen G₆ unchanged.
2026-09-19
Floor-map fiber handoff hosted; 0.2 cover files not supplied
Hosted the 19 September 2026 fiber handoff DOCX (38,901 bytes, SHA-256 6d79cdde…) and Appendix B checker verify_handoff.py (6,701 bytes, SHA-256 9f7179c5…, matching Appendix C). This-archive Python 3.11.2 on 2026-09-19T11:18:30Z: RESULT PASS, identical stdout under normal, -O, and -OO (450 bytes, SHA-256 bb883207…). Seed blocks, not cosets. Reported 0.1 files and 0.2 certificate/COVER.json were not supplied and are not authenticated. Not a source paper. Not a Navier–Stokes or geometry theorem. Papers remain seven. Frozen G₆ unchanged.
2026-09-19
Navier–Stokes geometric extension updated to Version 3.0; not a source paper
Hosted OMEGA_NS_Geometric_Extension_v3.pdf as received (2,376,354 bytes, SHA-256 98a3f747…). That digest does not match the revision-notes claim 42802e00…; the file also embeds a Content Credentials attachment. The eight intended supplements match the notes, including verify_omega_ns.py (f054d343…), audit_omega_sources.py (7bb07240…), test_omega_auditor.py (9cae8025…), TeX (2cadfed8…), author record (095d0549…), Lean DOCX (275da4ea…), and Julia ZIP (ef8f1eb7…). This-archive Python 3.11.2 / SymPy 1.14.0 on 2026-09-19T11:01:17Z: verifier 62 exact checks (identical under -O/-OO), auditor accepts the original package, mutation harness 38/36 PASS. Distinct from the author record (Python 3.12.14). No pdflatex rebuild. No fresh Lean or Julia run. Extension 1.0 remains under /extension/v1/. Papers remain seven. Frozen G₆ unchanged. Paper VI cubature certificates were not rerun. SRSD remains frozen.
2026-09-18
Navier–Stokes geometric extension 1.0 hosted; not a source paper
Hosted OMEGA_NS_Geometric_Extension.pdf (395,411 bytes, SHA-256 fc66480b…) and verify_omega_ns.py (6,622 bytes, SHA-256 d6dfd762…). This-archive Python 3.10.21 / SymPy 1.14.0 on 2026-09-18T03:41:44Z: 34/34 exact checks, identical stdout under normal, -O, and -OO (1,700 bytes, SHA-256 e39a48e3…). Similarity transport preserves (G+C)/a=φ+π; anisotropic branch realizes M²/A²; curl localization is a written existence proof, not a simulation. Not Paper VII rewritten. Not a blowup result. Not historical novelty. Paper VI cubature certificates were not rerun. SRSD remains frozen. Papers remain seven. Frozen G₆ bytes unchanged.
2026-09-17
Synthesis 1.0 focused claim check hosted; PDF not supplied
Hosted omega_synthesis_claim_check.py (4,891 bytes, SHA-256 9397c530…). This-archive Python 3.11.2 on 2026-09-17T19:30:11Z: normal, -O, and -OO all exit 0 with identical stdout (434 bytes, SHA-256 a6e768c3…): first disagreement 42189065; Sacks m=1, k=5/2 enclosure; streaming s=1/2 counterexample; 72 integer streaming examples. OMEGA_Synthesis(3).pdf was not attached; claimed SHA-256 01f0d19c… is unverified here. Integer hypotheses for the Sacks finite-error identity and streaming byte quotients, and composition notation for iteration, are recorded as printed corrections. Not an eighth paper. Not Lean. Not cubature. Not independent third-party reproduction. Papers remain seven. Frozen G₆ bytes unchanged.
2026-09-17
Blank notebook: history of computer languages
Added /notes and /notes/languages as a personal learning shell: decade slots, proof-assistant track, sources, and open questions, all marked to be written. Markdown twin at /notes/languages.md. Not a source paper, not MACHINE evidence, and not a history of OMEGA NAUGHT. Papers remain seven. Frozen G₆ bytes unchanged.
2026-09-13
Canonical frame figure for the arc-and-feet object
Added an oriented-frame drawing of the existing Paper VII object: u=(0,−1,0) down, v=(1,0,0) right, w=−u, baseline y=−ac parallel to v and not through α. Exact radii ρ0=a, ρ1=a√(2(1+s)), ρ2=aφ√(3+2s). Small-angle 2as≈aε is labeled as an approximation. A generated overlay JPEG is hosted; its garbled labels, non-true inset numerals, and ρ2-without-φ are not used as sources. Not a new object. Papers remain seven. Frozen G₆ unchanged.
2026-09-13
Arc-and-feet figure: marks on y=−ac, not a diameter
Homepage and geometry now draw the existing Paper VII object Γ as the supplied arc-and-feet diagram: blue major arc, green left foot, orange right foot, dashed seed chord omitted from Γ. Six marks on y=−a cos(ε/2), not a diameter through α. Consecutive separations aφ, a, 2as, a, aφ. 12° display; true ε=1″. Copy-pasteable Julia omega_local_geometric_object.jl and this-archive Julia 1.11.6 stdout hosted under /geometry/kernel/, with the author diagram JPEG. Not a new object or discovery. Does not enlarge Paper VII. Cubature packets, Lean lake PASS, f=22 r2 guard, and frozen G₆ bytes unchanged. Papers remain seven.
2026-09-13
Recovered cubature 10–21 and 23–24 exact packages hosted
The 74-file cubature evidence package was recovered from OMEGA_NAUGHT_Complete_Data.docx (3,721,530 bytes, SHA-256 279eacb0…). EXTRACT PASS: 74/74, manifest SHA-256 71d9d4ac…. Hosted originals: ClassI_Cubature_f23_f24_exact_certificate_v1.1.json 1,407,835 / e886510e…; verify_ClassI_f23_f24_exact_v1.1.py 6,818 / 41d83727…; ClassI_Cubature_f23_f24_verification_ledger_v1.1.txt 10,905 / 4d56dc2c…; replay_recovered.py 1,621 / a3bf98e7…; classI_exact_certificates_f2_f21.json 1,815,267 / 7b3945ad…; historical verifier 4,102 / 7c3cd105…; r2 11,383 / 4af07ac2…. Per-frequency records /cubature/frequencies/f10.json–f21.json, f23.json, f24.json. This-archive Python 3.11.2: r2 ALL PASS (383 identities), replay ALL PASS (109 identities), python3 -O refused. Author-supplied evidence_* transcripts are hosted separately under /cubature/evidence/2026-09-13-word-recovery/. Printed f=23,24 audit extract and LaTeX-emitted JSON 3ecbf665… remain distinct. Does not enlarge Paper VI (range remains 1≤f≤9). No maximality. Not peer review. Not independent third-party reproduction. Geometry generated/ recipe, f=22 r2 python3 -O guard, Paper IV five-design wording, and Lean lake PASS on this archive are preserved. Papers remain seven. Frozen G₆ bytes unchanged. Artifact count 218.
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.