Implementation Specification · Version 1.0 · 23 August 2026

Global Mathematical Object Conformance Specification

Matthew Alan Newman · ORCID 0009-0007-5468-3125 · Papers I–VI

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.

Source corpus

The Papers I–VI global object

The tuple notation is organizational. It does not assert that every component is derived from every other component.

Foundational boundary

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.

Quantized and rational floor dynamics

Paper I uses λ_Ω = φ / (φ+π) and the general quantizer Q_h(y) = h ⌊y/h⌋. The symbol τ is already fixed as Ω₀⁻¹; it is not the Paper-I spacing. Paper II specializes to

OMEGA arithmetic

This is an exact coefficient-field interoperability map. It is not the source of the icosahedral geometry, invariant moment equations, or positive cubature coefficients.

Radial icosahedral geometry and cubature

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.

Finite OMEGA replay

Conditional on the published strict enclosure of λ_Ω,

Machine contracts

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. Host-sensitive names such as .manifest are served as .txt under the versioned retrieval rule GET /releases/G6_RELEASE_1.1/files/{served_as or path}. The ZIP is optional transport; the authoritative file set is ZIP-independent.

/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

Canonical cross-runtime record

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.

Three distinct verification statuses

1. Mathematical theorem validity — rests on the proofs in the six source works; it is not certified by this conformance system.
2. Certificate replay — exact finite consequences: Qd = Sd′ + ρ, the 2¹⁵ floor identities, d*, cubature hashes, positivity, affine family.
3. Runtime conformance — a runtime passes when it executes the declared machine contract.

The preferred terminal wording is

GLOBAL OBJECT CONFORMANCE = PASS

rather than the stronger and potentially ambiguous phrase GLOBAL OBJECT = VERIFIED.

Target terminal report

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

Dependency discipline

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.

Canonical hash preimages

SHA-256 values are of explicit UTF-8 preimages: no BOM, no terminal newline, compact JSON separators "," and ":", published key order. See HASHING.json.

• The status-record digest 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 payload array of {path, sha256, bytes}.
• The release trust anchor is the SHA-256 of the RELEASE.json envelope, which is intentionally not listed in files[].
• The canonical field cubature = PASS means certificate replay for 1 ≤ f ≤ 9.

Clean-room reconstruction

Use CLEANROOM.json as the authoritative file list. An optional ZIP mirror G6_CLEANROOM_INPUT_v1.1.zip may be used as transport. The isolated surface is /cleanroom; do not give the evaluator the general homepage. 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.

License and versioning

Authored papers, documentation, and data are CC-BY-4.0; code is MIT (LICENSE, LICENSE-CODE). Imported DOI records keep their original licenses. Bytes belonging to a published identifier are never silently changed; any correction produces a new release identifier (VERSIONING.md). G6_RELEASE/1.1 is frozen unarchived. External archival on Zenodo is an author deposit of the payload files or of an optional ZIP; this companion does not mint a DOI (DEPOSIT.md).

Status of version 1.0

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

Frozen contracts are not rewritten. Paper VI is attached as C_cub on the same Class-I geometry.