This specification organizes six DOI-archived mathematical works into a single typed mathematical object while preserving their published dependency boundaries. Scale-Resolved State Dynamics (SRSD) remains the sole frozen foundational layer. Quantized dynamics, rational floor dynamics, radial icosahedral geometry, OMEGA arithmetic, finite replay, and exact positive cubature remain separately typed components.
The purpose of the implementation is not to replace the proofs in the underlying papers. It is to provide reproducible machine conformance: independent Rust and Julia implementations must replay the declared exact finite certificates, preserve the exact arithmetic interfaces, and emit the same canonical global conformance record.
The existing OMEGA_NAUGHT/1.0 implementation contract is treated as a frozen subordinate contract and is not modified by the Papers I–VI extension. Paper VI contributes a separate cubature component and its own machine-readable exact data.
| Work | DOI |
|---|---|
| I. Newman’s Quantized Omega Contraction Theorem | 10.5281/zenodo.21830285 |
| II. Ordered Euclidean Remainders… | 10.5281/zenodo.21843485 |
| III. Scale-Resolved State Dynamics v1.0 | 10.5281/zenodo.21927248 |
| IV. Radial Icosahedral Sampling… | 10.5281/zenodo.22033917 |
| V. OMEGA NAUGHT Ω₀ | 10.5281/zenodo.22048540 |
| VI. Exact Positive Icosahedral Cubature… | 10.5281/zenodo.22068873 |
| Sort | Role |
|---|---|
| S_SRSD | frozen exact scale-resolution foundation |
| A_Ω | OMEGA arithmetic and exact symbolic representation |
| D_quant | floor-quantized contraction dynamics |
| D_rat | rational floor dynamics and Euclidean remainders |
| H_ico | radial Class-I icosahedral geometry and invariant harmonics |
| C_fin | finite exact replay, canonical records, and machine certificates |
| C_cub | positive fixed-Class-I cubature for the proved range 1 ≤ f ≤ 9 |
| J₆ | explicit typed interfaces between the above sorts |
The tuple notation is organizational. It does not assert that every component is derived from every other component.
SRSD remains the sole frozen foundation. For a positive scale vector s and a state y,
No OMEGA constant, floor-dynamical specialization, icosahedral construction, cubature rule, finite-limb convention, or implementation language is promoted to an additional foundation.
Paper I uses λ_Ω = φ / (φ+π) and Q_τ(y) = τ ⌊y/τ⌋. Paper II specializes to
This is an exact coefficient-field interoperability map. It is not the source of the icosahedral geometry, invariant moment equations, or positive cubature coefficients.
For 1 ≤ f ≤ 9 the exact algebraic degrees are 5, 9, 11, 15, 17, 21, 23, 27, 29. The all-frequency continuation is not part of the proved object:
At f = 9 the invariant moment system has rank 11 with 12 orbit variables:
ν_f and μ_f share the nodes X_f and are not identified. SRSD transports an already proved cubature rule; it does not derive it.
Conditional on the published strict enclosure of λ_Ω,
SRSD foundational specification
│
├── OMEGA_NAUGHT/1.0 [frozen]
│
└── CLASS_I_CUBATURE/1.0
│
└────────────┐
│
NEWMAN_GLOBAL_OBJECT/1.0
These implementation identifiers do not replace the titles, versions, or DOIs of the mathematical papers.
Machine-readable copies of the nested contracts are published as JSON
(application/json) and as plain-text .txt
(text/plain; charset=utf-8). Independent fetchers should use
those. The .manifest filename is archival inside the freeze ZIP;
some hosts map that extension to HTML5 AppCache.
/g6/CLASS_I_CUBATURE_1_0.json /g6/CLASS_I_CUBATURE_1_0.txt /g6/NEWMAN_GLOBAL_OBJECT_1_0.json /g6/NEWMAN_GLOBAL_OBJECT_1_0.txt
Rust, Julia, and the live TypeScript companion emit the same no-space JSON. cubature_frequency_max and first_mismatch are JSON numbers.
{"contract":"NEWMAN_GLOBAL_OBJECT/1.0","srsd":"PASS","quantized_dynamics":"PASS","rational_floor":"PASS","omega":"PASS","icosahedral_geometry":"PASS","cubature":"PASS","finite_replay":"PASS","interfaces":"PASS","cubature_frequency_max":9,"first_mismatch":42189065,"result":"PASS"}
SHA-256 of that UTF-8 string:
Cross-runtime conformance requires h_Rust = h_Julia = h_Web. The Web
implementation is the frozen TypeScript snapshot at g6/web/,
hashed in WEB_PIN.json. The live site demonstrates that snapshot;
it is not an unpinned extra runtime.
The preferred terminal wording is
GLOBAL OBJECT CONFORMANCE = PASS
rather than the stronger and potentially ambiguous phrase GLOBAL OBJECT = VERIFIED.
NEWMAN GLOBAL MATHEMATICAL OBJECT contract: NEWMAN_GLOBAL_OBJECT/1.0 SRSD foundation ....................... PASS Quantized contraction ................. PASS Euclidean reconstruction .............. PASS Rational-floor exact replay ........... PASS Class-I geometry ...................... PASS OMEGA quadratic arithmetic ............ PASS 15-bit exact replay ................... PASS First disagreement certificate ........ PASS Cubature f=1..9 ....................... PASS Frequency-9 affine family ............. PASS Frequency-9 positivity interval ....... PASS Orbit-mass max-min .................... PASS Per-node max-min ...................... PASS Q(sqrt(5)) -> OMEGA interface ......... PASS Cubature -> SRSD transport ............ PASS Canonical record ...................... PASS Cross-runtime hash .................... PASS PROVED CUBATURE DOMAIN: f = 1..9 OPEN CUBATURE DOMAIN: f >= 10 GLOBAL OBJECT CONFORMANCE = PASS
The final arrow is representational. It must not be reversed into a claim that Ω₀, λ_Ω, the 15-bit floor bridge, or SRSD generated the cubature theorem.
SHA-256 values are of explicit UTF-8 preimages: no BOM, no terminal newline,
compact JSON separators "," and ":", published key
order. See HASHING.json.
92187a21… commits to the entire canonical conformance record, not to the underlying evidence artifacts.evidence_sha256 14fea940… is SHA-256 of the four-field compact object (Omega manifest, both CSVs, status record).inventory_sha256 is SHA-256 of the compact files array.Use G6_CLEANROOM_INPUT_v1.0.zip. That archive contains papers, specification, contracts, certificates, and data. It does not contain the reference implementations. Printing the publicly known hash is not success. The implementation must derive the intermediate evidence and only then emit the canonical record. Protocol: CLEANROOM.md.
CC-BY-4.0 applies to papers, data, site text, and code alike (LICENSE). Bytes belonging to v1.0 are never silently changed; any correction produces a new release identifier (VERSIONING.md). External archival on Zenodo is an author deposit of the ZIP; this companion does not mint a DOI (DEPOSIT.md).
The mathematical source corpus is fixed by the six cited DOI records.
The existing OMEGA implementation contract remains frozen.
Independent Rust, Julia, and TypeScript runners replay the published Paper-VI CSV
certificates (orbit masses SHA-256 eed325c5…, f=9 family SHA-256
851a5ff0…), the affine family W(t), the exact positivity interval
t_L < t < t_U, the witness t = 1/27, and both max–min members.
Native reconstruction of the spherical invariant moment matrices is not required
for this certificate-replay conformance step.
GLOBAL OBJECT CONFORMANCE = PASS