Registry
Evidence for a selected claim
8 source works are registered. 69 claims are listed with their own mathematical status and implementation scope. Written proofs, formal builds, exact checks, and file hashes are not interchangeable.
| Claim | Branch | Mathematical status | Implementation | Record |
|---|---|---|---|---|
| Equal-weight harmonic obstruction | cubature | theorem claim | not applicable | harmonic-obstruction |
| Positive cubature exactness for 1 ≤ f ≤ 9 | cubature | theorem claim | pass | cubature-f1-f9-exactness |
| Positivity of orbit masses for 1 ≤ f ≤ 9 | cubature | theorem claim | pass | cubature-f1-f9-positivity |
| Target-degree exactness for 10 ≤ f ≤ 21 | cubature | certificate-backed post-publication computation; not part of Paper VI v1.3 | pass | cubature-f10-f21 |
| Target-degree exactness on the fixed frequency-10 Class-I grid | cubature | certificate-backed post-publication computation; not part of Paper VI v1.3 | pass | cubature-f10 |
| Target-degree exactness on the fixed frequency-11 Class-I grid | cubature | certificate-backed post-publication computation; not part of Paper VI v1.3 | pass | cubature-f11 |
| Target-degree exactness on the fixed frequency-12 Class-I grid | cubature | certificate-backed post-publication computation; not part of Paper VI v1.3 | pass | cubature-f12 |
| Target-degree exactness on the fixed frequency-13 Class-I grid | cubature | certificate-backed post-publication computation; not part of Paper VI v1.3 | pass | cubature-f13 |
| Target-degree exactness on the fixed frequency-14 Class-I grid | cubature | certificate-backed post-publication computation; not part of Paper VI v1.3 | pass | cubature-f14 |
| Target-degree exactness on the fixed frequency-15 Class-I grid | cubature | certificate-backed post-publication computation; not part of Paper VI v1.3 | pass | cubature-f15 |
| Target-degree exactness on the fixed frequency-16 Class-I grid | cubature | certificate-backed post-publication computation; not part of Paper VI v1.3 | pass | cubature-f16 |
| Target-degree exactness on the fixed frequency-17 Class-I grid | cubature | certificate-backed post-publication computation; not part of Paper VI v1.3 | pass | cubature-f17 |
| Target-degree exactness on the fixed frequency-18 Class-I grid | cubature | certificate-backed post-publication computation; not part of Paper VI v1.3 | pass | cubature-f18 |
| Target-degree exactness on the fixed frequency-19 Class-I grid | cubature | certificate-backed post-publication computation; not part of Paper VI v1.3 | pass | cubature-f19 |
| Target-degree exactness on the fixed frequency-20 Class-I grid | cubature | certificate-backed post-publication computation; not part of Paper VI v1.3 | pass | cubature-f20 |
| Target-degree exactness on the fixed frequency-21 Class-I grid | cubature | certificate-backed post-publication computation; not part of Paper VI v1.3 | pass | cubature-f21 |
| Positive degree-69 rule on the fixed frequency-22 grid | cubature | certificate-backed theorem claim | pass | cubature-f22-degree69 |
| Degree-70/71 obstruction on the fixed frequency-22 grid | cubature | obstruction | pass | cubature-f22-obstruction |
| Strictly positive H₃-invariant rules on X₂₃ and X₂₄ | cubature | theorem claim | pass | cubature-f23-f24-existence |
| Rank and affine dimension four on the f=23 and f=24 moment systems | cubature | corollary | pass | cubature-f23-f24-rank |
| Existence of strictly positive H_3-orbit-constant rules of target degree t_f for every f ≥ 25 | cubature | conjecture | not applicable | cubature-f23-conjecture |
| Typed exact interfaces among Papers VII, V, I, II and frozen SRSD | network | theorem claim | not run | typed-network-interfaces |
| Ω₀ reference identities | omega0 | definition | pass | omega0-definitions |
| Cross-language replay of the frozen G₆ canonical record | integration | standard consequence | pass | g6-cross-language-replay |
| OMEGA_NAUGHT/1.0 Python, Julia, Java, and Rust conformance | integration | standard consequence | pass | omega-naught-1-0-jprv |
| First floor-map disagreement at 42189065 | dynamics | certificate-backed finite exact fact | pass | floor-first-disagreement |
| Exact 15-bit admissible interval and constrained optima | dynamics | certificate-backed finite exact facts | pass | successor-I15 |
| No accepted successor contract | dynamics | status statement | not applicable | successor-not-accepted |
| Omega-Alpha finite integer kernel and codebooks | dynamics | exhaustively verified finite facts in the locally hosted synthesis | pass | omega-alpha-15bit-kernel |
| Omega-Alpha is not a source paper | dynamics | status statement | not applicable | omega-alpha-not-source |
| Construction-to-OMEGA uniqueness of the marked kernel | geometry | theorem claim | not applicable | geometry-local-closure |
| Three fundamental bearings and the complete center-angular law | geometry | theorem claim | not applicable | geometry-angular-fan |
| Exact 3D reconstruction and positive-homothety family | geometry | theorem claim | not applicable | geometry-center-relative |
| Notebook outer scaffold is an adopted transcription; remaining completion is not claimed | geometry | adopted definition plus derived identities in the Zenodo preprint; remaining outer completion is a status statement | not applicable | geometry-outer-scaffold |
| Experimental 4D OMEGA rotation is not a privileged memory anchor | geometry | numerical experimental control; not a theorem | not applicable | geometry-drift-control |
| Kernel construct node log and presentation machine | geometry | implementation interface around Paper VII; not a theorem and not a second evaluator | pass | geometry-construct-interface |
| De-branded executable audit of typed maps | network | executable mathematical audit of de-branded maps; not a joining theorem and not a formal proof-assistant kernel | pass | typed-connection-audit |
| Lean 4 formalization of a selected geometric-provenance measurement | formalization | author-supplied Lean 4 formalization of a selected geometric-provenance measurement; hosted sources match package SHA256SUMS; lake build PASS on this archive 2026-09-13 (build.log SHA-256 ddc10580…); axiom audit 147 reports, axioms {propext, Classical.choice, Quot.sound}; Python axiom-coverage PASS; not a joining theorem, not peer review, and not independent reproduction of Papers I–VII | pass | lean-provenance-formalization |
| Julia mathematical proof companion of a selected geometric-provenance measurement | formalization | companion software 0.1.0 / package v0.1: written proofs plus exact finite certificates corresponding to 147 Lean declarations; hosted 68 members recovered from the Word transcription match SHA256SUMS byte-for-byte; 29 Lean reference files are byte-identical to /formal/; author-supplied Julia 1.11.6 O0/O3 exit 0 is archived evidence, not a run on this archive; not a joining theorem, not an additional source paper, not peer review, and not independent reproduction of Papers I–VII | not run | julia-proof-companion |
| Volume-preserving fluid transport of a marked OMEGA set | extension | theorems proved in locally hosted Version 3.0; not a source paper | pass | omega-ns-geometric-extension |
| Frozen rational floor map: fibers, depth layers, and 32-block seed cover | dynamics | theorems proved in the locally hosted 19 September 2026 handoff; independent stdlib replay PASS; reported 0.2 ledger files not supplied | pass | omega-fiber-structure |
| paper 8: exact arithmetic certification of geometric reconstruction and transport | certification | written theorems in the 19 September 2026 Zenodo preprint 10.5281/zenodo.22848213; this-archive Python replay of the finite certificate is not a proof-assistant check of the analytic theorems 19 September 2026 localized-flow audit hosted at /papers/8/audit-01 is additional work covering Theorems 7.3–7.6 and 8.6; it is not peer review. | not applicable | paper-8-certification |
| paper 8 localized forced incompressible flow (Theorems 7.3–7.6 and 8.6) | certification | written theorems in the 19 September 2026 preprint; 19 September 2026 audit found no proof-breaking defect in Theorems 7.3–7.6 or 8.6. Audit is not institutional peer review and does not establish priority of the combined methods. | pass | paper-8-localized-flow-audit |
| Six-mark projective recognition, landmark decoding, and baseline integration bounds | geometry | written additional consequences developed in exploration 02 using established methods. Not a theorem of Paper VII. Canonical seed remains one arcsecond. Priority of the applications is not assessed. | pass | omega-object-exploration-02 |
| Positive quadrature classification for the symmetric six-node family | geometry | Written proofs in PROOFS.md. Computational checks corroborate selected identities. Not a theorem of Paper VII. Canonical seed remains one arcsecond. | pass | omega-sampling-quadrature |
| Boundary reconstruction, volume-preserving transport, and an invariant cubic | geometry | Written proofs in the 21 September 2026 PDF and the 22 September 2026 remarks. Not a theorem of Paper VII. Not a source paper. | pass | omega-boundary-reconstruction |
| Explicit minimal ten-sample reconstruction of H≤2 ⊕ ℝJ | geometry | Written supplementary note, 23 September 2026. Not a theorem of Paper VII and not an additional counted source paper. Ten is minimal for scalar point samples on this space. The thirteen-sample arrangement's three consistency equations are not an error-correction guarantee. General transport is the written argument; two rational executions are finite checks. | pass | omega-ten-sample-reconstruction |
| Exact field interface for the golden algebra | geometry | Supplementary note, 25 September 2026. Established field arithmetic and its specified application to existing OMEGA objects. Not an additional source paper. The checker does not prove the Galois correspondence or the transcendence of pi. | pass | omega-exact-field-interface |
| 399 rational-floor reference kernel | dynamics | Explanatory supplement for the map already published on /dynamics and used by the reconstruction tool. Not a new theorem and not an additional source paper. A valid suffix is another seed. | pass | omega-floor-kernel-399 |
| General integer floor transition | dynamics | Standard Euclidean division, written as an application record. Not a new theorem and not an amendment of Papers I–III. | pass | floor-transition-general |
| Ellipse and operator note, documentation only | geometry | Documentation of a hosted derived note. Not a theorem status, not a Paper VII amendment, and not an additional source paper. | not run | operator-bridge-note |
| Six-mark sampling polar, with a conditional packing | geometry | Direct identities for the declared sampler and sample bound. The packing statement is conditional on two external hypotheses that this note does not establish. Not a source paper and not an amendment of Paper VII. | pass | sampling-polar-note |
| Transition invariants: symbolic identities and a finite ledger audit | geometry | An exact symbolic-algebra checker with a finite canonical-ledger audit. Both executions reproduce the declared checks. Neither establishes physical unification or independent mathematical review. | pass | transition-invariants |
| Self-similarity, numerical difference, and exact recovery | geometry | The hosted note states five conclusions and written arguments for them. This archive has not reviewed those arguments as a proof. The checker rerun reproduces the declared symbolic checks, rational certificates, and finite ledger audit. Not a source paper and not an amendment of Paper VII. | pass | core-theorem-note |
| Integration proof bundle, 14 October 2026 | geometry | The hosted ledger states written arguments. This archive has not reviewed them as a proof. The Python checker was rerun and reproduced the declared algebra checks and finite audit. Not a source paper, not an amendment of Paper VII, and not a certificate of an external mathematics release. | pass | integration-proofs |
| Relative representation and recoverable information, 15 October 2026 | geometry | The hosted thesis states written arguments. This archive has not reviewed them as a proof. A transcription of the printed checker was rerun and reproduced the declared symbolic checks and finite audits. Not a source paper, not an amendment of Paper VII, and not a certificate of the unseen companion bytes. | pass | relative-representation |
| Supplementary workflows: canonical readouts, integer witnesses, and degree-2 transfer | geometry | The checker proves the inverse formulas as linear forms, the Smith identity, and the Gram and transfer identities on the declared grids. The classical cyclotomic degree formula is cited and is not reproved. Not a reviewed proof of that formula, not a proof-assistant certificate, not peer review, and not an amendment of Paper VII. | pass | supplement-1-workflows |
| Selected scale compatibility | dynamics | Written note. Not reviewed as a proof. Not a source paper. | not applicable | geometry-scale-compatibility |
| Observation fibers and recoverable relationships | dynamics | Written note. Not reviewed as a proof. Not a source paper. | not applicable | reference-recovery-note |
| Reference-recovery checker, site run of 24 October | geometry | Implementation record of a named script. Not a proof review and not peer review. | pass | reference-recovery-checker |
| Scalar reference language v0.1 | dynamics | Specification note. Not a proof that the decoder authenticates a sender. | not applicable | omega-language-v0-1 |
| 600-cell real signal model | dynamics | Written all-domain statement under the definitions. Not reviewed as a proof. The planar geometry does not select this coupling. | not applicable | cell600-real-dynamics |
| Full-remainder inverse on the integer network | dynamics | Written all-integer statement. Not reviewed as a proof. Quotient agreement is not remainder equality. | not applicable | cell600-full-remainder |
| Modulo-8 joint witness | dynamics | Written theorem plus a historical checker record. The written argument was not reviewed. The 431-bit midpoint method remains correct in its restricted sharpness. 306 bits is not a necessity on the canonical cube. | pass | cell600-mod8-witness |
| 306-bit lower bound on the unbounded domain | dynamics | Written counting argument. Not reviewed. Not a codec optimality theorem. | not applicable | cell600-306-bit-bound |
| Ten-step extinction on the canonical cube | dynamics | Written domain statement. Not an enumeration and not a validity limit at horizon 23. | not applicable | cell600-ten-step-extinction |
| Canonical network parameter interval | dynamics | Exact finite certificate plus the local-attainability argument. The written necessity argument was not reviewed. This does not amend the scalar successor contract. | pass | cell600-parameter-interval |
| Positive-simplex corollary | dynamics | Written derived result. No execution status and no formal status are inherited. | not applicable | cell600-positive-simplex |
| Decoder cost is not a polynomial-time claim | dynamics | Finite observations plus an exponential worst-case bound. Not a polynomial-time theorem. | not applicable | cell600-decoder-budget |
The 26 October joint-witness stdout is a historical record (Python 3.12.14). The 27 October parameter certificate was rerun on this archive and is a separate file. Neither record is a review of the written arguments, a Lean proof, or an issued publication. 600-cell reproduction.
Supplementary records from 24 October 2026 are not additional source works. The restored reference proofs and compatibility proofs are written arguments. The reference-recovery page records this archive’s Python 3.10.21 run of the restored checker. That run is an implementation check, not a review of the arguments.
The historical checker download is not a standalone run. That page keeps the unchanged 23 September script and directs you to the runnable ZIP omega-workbench-impl-2026-09-25-r3.zip (execution record). The r2 ZIP omega-workbench-impl-2026-09-25-r2.zip and the 20:31:42Z snapshot omega-workbench-impl-2026-09-25.zip are unchanged.
Status matrix · Reproduction recipes · claims.json · Workbench repair checks, 23 September 2026