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\newcommand{\SRSD}{S_{\mathrm{SRSD}}}
\newcommand{\AO}{A_{\Omega}}
\newcommand{\Dquant}{D_{\mathrm{quant}}}
\newcommand{\Drat}{D_{\mathrm{rat}}}
\newcommand{\Hico}{H_{\mathrm{ico}}}
\newcommand{\Cfin}{C_{\mathrm{fin}}}
\newcommand{\Ccub}{C_{\mathrm{cub}}}
\newcommand{\Qfive}{\mathbb{Q}(\sqrt{5})}
\newcommand{\Omzero}{\Omega_0}
\title{\textbf{Global Mathematical Object Conformance Specification}\\[0.35em]
\large Papers I--VI, Frozen Dependency Boundaries,\\
Parallel Rust and Julia Reference Implementations,\\
and Canonical Cross-Runtime Replay}
\author{Matthew Alan Newman\\
\small ORCID: 0009-0007-5468-3125}
\date{23 August 2026\\[0.25em]
\small Implementation Specification, Version 1.0}
\begin{document}
\maketitle
\begin{abstract}
This specification organizes six DOI-archived mathematical works into a
single typed mathematical object while preserving their published dependency
boundaries. SRSD remains the sole frozen foundational layer. The existing
\texttt{OMEGA\_NAUGHT/1.0} contract is treated as a frozen subordinate
contract. Paper VI contributes a separate cubature component
\texttt{CLASS\_I\_CUBATURE/1.0}. The cross-component contract is
\texttt{NEWMAN\_GLOBAL\_OBJECT/1.0}.
\end{abstract}

\section{The Papers I--VI Global Mathematical Object}
\[
G_6=
\bigl(
\SRSD,\,
\AO,\,
\Dquant,\,
\Drat,\,
\Hico,\,
\Cfin,\,
\Ccub;\,
J_6
\bigr).
\]
Foundational identity: $D_sE_s=\mathrm{id}$.
Rational floor: $Qd_k=Sd_{k+1}+\rho_k$ with $Q=339949771344778$, $S=10^{15}$.
Omega channel: $a+b\sqrt5\mapsto(a-b)+(2b/T)\lambda$.
Class-I nodes: $|X_f|=10f^2+2$.
Cubature degrees for $1\le f\le9$: $5,9,11,15,17,21,23,27,29$.
Frequency nine: $W(t)=W^{\mathrm{part}}+tW^{\mathrm{null}}$, $t_L<t<t_U$, witness $t=1/27$.
Fifteen-bit bridge on $D_{15}$; first disagreement $d^\ast=42189065$.
$f\ge10$ remains open.

\section{Machine contracts}
\[
\mathrm{SRSD}\;\to\;
\{\texttt{OMEGA\_NAUGHT/1.0},\;\texttt{CLASS\_I\_CUBATURE/1.0}\}
\;\to\;
\texttt{NEWMAN\_GLOBAL\_OBJECT/1.0}.
\]
Cubature CSV pins:
\texttt{eed325c55fe183b36b46b591f758935bcf748a91c2427a09a965337895354b98}
and
\texttt{851a5ff03452e21f7839285cd63423385c936907568e852a174056197c20a95f}.

\section{Canonical record}
The no-space JSON record has SHA-256
\texttt{92187a21a7ad8ecef384eda3a654aaa49daf46a31422e168eb5871d218c949fa}.
Preferred wording: \texttt{GLOBAL OBJECT CONFORMANCE = PASS}.

\section{Three statuses}
Mathematical theorem validity — rests on the proofs in the six source works;
it is not certified by this conformance system.
Certificate replay is exact finite computation.
Runtime conformance is independent Rust, Julia, and the pinned TypeScript
snapshot of the declared contracts.
The live website demonstrates that snapshot; it is not an unpinned extra runtime.


\end{document}