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\begin{document}

\title{Chirality from $\hthree$: Standard Model Gauge Group\\
and Chiral Representation from Self-Modeling\\
via Exceptional Jordan Algebra}

\author{Bryan Ehrlich}
\affiliation{Independent researcher}

\date{\today}

\begin{abstract}
Self-modeling---the requirement that a physical system contains a
faithful model of itself---forces quantum mechanics with
$M_n(\mathbb{C})^{sa}$ state spaces~\cite{Paper5}. We argue that the
exceptional Jordan algebra $\hthree$ is the unique candidate for the
``universe algebra'' via its non-composability (it cannot be a subsystem of
a larger system). A C*-observer probing $\hthree$ induces a Peirce
decomposition under a rank-1 idempotent $E_{11}$, and we argue that the
observer's C*-algebra nature motivates complexification of the Peirce
half-space, canonically upgrading the symmetry from $\Spin{9}$ to
$\Spin{10}$ acting on a 16-dimensional complex Weyl spinor $\Stenplus$.
A single additional algebraic choice---a complex structure $u \in S^6
\subset \mathrm{Im}(\mathbb{O})$---simultaneously determines both the
Standard Model gauge group $\SMgauge$ via $\Ffour$ intersection and the
chiral (left-handed) fermion representation via the $\Cl{6}$ volume form.
The result is conditional on three inputs beyond the self-modeling axioms
(the identification of $\hthree$, the choice of idempotent, and the choice
of complex structure) plus a conjectural complexification principle whose
formalization remains open.
We present the 9-link chain from self-modeling axioms to a one-generation
chiral Standard Model representation, with explicit classification of each
link as proved, argued, or an open gap.
\end{abstract}

\maketitle

\input{sections/introduction}
\input{sections/complexification}
\input{sections/chirality}
\input{sections/synthesis}
\input{sections/gaps}
\input{sections/discussion}

\begin{acknowledgments}
[Acknowledgments placeholder.]
\end{acknowledgments}

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