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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}(\sqrt5)}

\title{\textbf{OMEGA NAUGHT Site Update Data}\\[0.3em]
\large Papers I--VI / $G_6$ Additive Extension}
\author{Matthew Alan Newman}
\date{23 August 2026}

\begin{document}
\maketitle

\section*{Purpose}

This file contains the data needed to update the live OMEGA NAUGHT site from the
existing Papers I--V global object to the Papers I--VI object. The update is
\textbf{additive}. The existing \texttt{OMEGA\_NAUGHT/1.0} contract is retained
unchanged. Paper VI is added as a distinct positive-cubature component, and a
new global assembly is displayed above the existing subordinate components.

\section*{1. Existing Frozen Contract: Keep Unchanged}

\begin{lstlisting}
contract=OMEGA_NAUGHT/1.0
algebra=Q(T)[lambda]/(lambda^2-T*lambda-T^2)
bits=15
Q=339949771344778
S=1000000000000000
L60=339949771344778929576702809321279193551009905014259416689444
U60=339949771344778929576702809321279193551009905014259416689445
\end{lstlisting}

Do not rename, rewrite, or reinterpret this existing contract as part of the
Paper-VI update.

\section*{2. Add Paper VI to the Publication Record}

\begin{lstlisting}
Paper VI
Author: Newman, M.
Year: 2026
Title: Exact Positive Icosahedral Cubature on Fixed Radial Class-I Grids:
       Quadratic-Field Interoperability, Exact Replay,
       and Typed Compatibility with Papers I-V
Repository: Zenodo
DOI: 10.5281/zenodo.22068873
\end{lstlisting}

\section*{3. Papers I--VI Global Object}

Replace the displayed Papers I--V assembly
\[
G_5=(\SRSD,\AO,\Dquant,\Drat,\Hico,\Cfin;J)
\]
with
\[
\boxed{
G_6=(\SRSD,\AO,\Dquant,\Drat,\Hico,\Cfin,\Ccub;J_6).
}
\]

\section*{4--14}

See the companion HTML for the cubature data, $f=9$ family, $\mathbb{Q}(\sqrt5)$
map, CSV hashes, machine contracts, and status language.

\end{document}