Home › Status Status SRSD EXTERNAL-AUDIT BOUNDARY — 30 AUGUST 2026 SRSD v1.0 is frozen and published. It is used only as an external arithmetic and resolution-audit instrument applied to separately defined theories. Older G₆ “global object,” “foundation,” and “gluing” language is retained solely as provenance for frozen implementation packages. It does not modify SRSD, merge the source theories, or define their current mathematical dependency structure. STANDARD MATHEMATICS AND CLAIM SCOPE — 30 AUGUST 2026 The primitive SRSD encoder and decoder use coordinatewise quotient–residual decomposition through the floor function, a standard mathematical construction. SRSD does not claim to invent division with remainder or to provide a new foundation for mathematics. “Foundational closure” refers only to the internal sufficiency of the frozen SRSD v1.0 specification for the systems it defines. The archive makes no blanket claim of novelty, priority, peer review, or independent validation. Any claim of originality must concern a specifically stated formulation or derived result and must be evaluated separately against the relevant prior literature. Publication status: six Zenodo preprints and one Zenodo report. Paper VII is version 1.6 at DOI 10.5281/zenodo.22233573. Not peer reviewed unless a specific work is later linked to a peer-reviewed publication. Computational reproducibility: exact verifiers and/or finite certificates are supplied where listed. Independent third-party reproduction: none recorded on this site unless a named reproduction and its public evidence are linked. Claim status. No cell is computed from another. Claim / object Paper / source Mathematical status Computational status Conformance status Paper I — quantized contraction I Source preprint; exact identities Named historical G₆ replay (implementation property) Not a theorem Paper II — rational floor maps II Source preprint; remainder ledgers Named historical G₆ replay (implementation property) Not a theorem Paper III — SRSD external audit instrument III Frozen v1.0. Foundational closure means internal sufficiency, not a new foundation for mathematics. Condensed listing supplied; not a theorem checker Not a theorem Paper IV — harmonic obstruction IV Every complete radial Class-I grid is a spherical five-design. The limiting equal-weight sampling measure differs from uniform spherical area first at harmonic degree six. Where supplied in cubature artifacts Not a theorem Paper V — Ω₀ reference identities V Source report; many identities definitional Exact notebooks and OMEGA_NAUGHT/1.0 replay Not a theorem Paper VI — cubature 1 ≤ f ≤ 9 VI Source preprint; exact moment systems. Independent of Ω₀ and SRSD. Frozen CSV replayed by historical G₆ Not a theorem Paper VII — marked kernel VII Construction-to-curve theorem: unique marked kernel from the one-arcsecond seed and sequential bilateral extensions. Complete center-angular fan; Gram rank two; exact R³ realization. Metric outer scaffold adopted; remaining completion not claimed. Companion generator evaluates closed formulas. Zenodo preprint v1.6. Not a theorem Paper VII — exact 3D reconstruction VII p_{j,σ}=α+a(c u+σ x_j v); SE(3) placement; (R>0,×) torsor on the scaled family. Companion JSON/OBJ generator. Not a theorem checker. Not a theorem Target-degree rules 10 ≤ f ≤ 21 VI addendum Unpackaged author result; not in the fully reproducible corpus No public certificate package; not a release-corpus object Not a theorem Frequency 22 on fixed X₂₂ f22 addendum Exact degree-69 positivity and 70/71 obstruction Python 3.12.13 PASS and Julia 1.11.6 PASS, separately Two-implementation PASS X₂₃ degree 71 and X₂₄ degree 75 locally hosted theorem Strictly positive H₃-invariant weights; no maximality; does not enlarge Paper VI Proof hosted; hash-pinned weights and verifier not enumerated Not run Existence of strictly positive H₃-orbit-constant rules for every f ≥ 25 open Open conjecture. Higher degrees at f=23 and f=24 are not shown impossible. Not applicable Not a theorem Typed network of exact interfaces locally hosted dossier Exact maps among VII–V–I–II and frozen SRSD; independent cubature junction. Not a joining theorem. Proof text hosted. Dossier’s embedded verifier is not a separate artifact. Not run (dossier verifier) De-branded typed-map audit locally hosted executable audit Executable audit of de-branded maps. Not a joining theorem. Radial identities are algebraic, not physics. Python 3.10.21 / SymPy 1.14.0 PASS: 32768 D₁₅ states, 32768×23 remainder reconstruction, seven negative paths Named runtime PASS; not independent reproduction Lean 4 geometric-provenance formalization locally hosted Lean 4 package Selected measurement of the specified marked construction. Not uniqueness among all measurements. Not a joining theorem. Sources hosted and hash-matched to SHA256SUMS. lake build PASS on this archive 2026-09-13. Python axiom-coverage PASS: 147 reports. lake build PASS on this archive; Python inventory PASS; not independent reproduction Julia mathematical proof companion locally hosted companion software Written proofs and exact certificates corresponding to the 147 Lean declarations. Selected measurement, not uniqueness among all measurements. Not a joining theorem and not an eighth source paper. Author-supplied Julia 1.11.6 O0/O3 records, six identical certificate files, 147 indexed declarations, 97 polynomial zero residuals, complete canonical-domain reconstruction. 68 members hosted; SHA256SUMS match. Not a run performed by this site. Not run on this archive 15-bit successor search (not a replacement contract) local audit Exact I₁₅, q_min, signed-32 bound, extinction Python runtime reference Not a theorem Omega/JPRV–SRSD terminology module v2.1.0 local module Portable JSON; first residual injective on D₁₅. v2.0.0 superseded. Exact integer checks in the module Not a theorem Omega-Alpha July 2026 synthesis (not a source paper) local package Scoped consolidation of earlier drafts omega_alpha_reference.py matched frozen report Not a theorem G6_RELEASE/1.1 cross-language replay legacy G₆ Not a theorem; historical packaging of named frozen outputs Rust, Julia, TypeScript Implementation PASS; not unification Implementation-conformance ledger (historical G₆) Implementation conformance: the named implementation reproduced the specified reference outputs. This does not establish theorem validity, peer-review status, or independent mathematical reproduction. Historical G₆ artifact: canonical record reproduced in Rust and Julia, with a pinned TypeScript browser replay. The G₆ Rust runner declares no third-party crates; cargo run --release --offline --locked is the named run. Implementation conformance of a frozen package, not a theorem joining the source theories. Separate OMEGA_NAUGHT/1.0 conformance: Python, Julia, Java, and Rust. Historical G₆ canonical-record runtimes. Language Role Status Artifact Rust Historical G₆ canonical record PASS rust/src/main.rs Julia Historical G₆ canonical record PASS julia/run.jl TypeScript Pinned browser snapshot PASS Historical G₆ artifact replay OMEGA_NAUGHT/1.0 conformance runtimes. Language Role Status Artifact Python OMEGA_NAUGHT/1.0 PASS omega_naught_conformance.py Julia OMEGA_NAUGHT/1.0 PASS omega_naught_conformance.jl Java OMEGA_NAUGHT/1.0 PASS OmegaNaughtConformance.java Rust OMEGA_NAUGHT/1.0 PASS omega_naught_conformance.rs Status of 10 ≤ f ≤ 21 Unpackaged author result for 10 ≤ f ≤ 21: not part of the fully reproducible release corpus. Maximality is not claimed. What this site does not claim The archive makes no blanket claim of novelty, priority, peer review, or independent validation. Some displayed identities are standard or definitional and are included to make the computational specification self-contained. Any claim of originality must concern a specifically stated formulation or derived result and must be evaluated separately against the relevant prior literature. Independent third-party reproduction: none recorded on this site unless a named reproduction and its public evidence are linked. G₆ packaging is not a theorem joining the theories. The tuple exists definitionally because unrelated typed objects can always be placed in a tuple. A canonical hash proves equality of a named byte string. Aggregating separate maps into interfaces=PASS is a historical implementation outcome, not current source-map discipline.
