% main.tex -- General Relativity from Self-Modeling on h_3(O)
% ASSERT_CONVENTION: natural_units=natural, metric_signature=mostly_minus,
%   jordan_product=(1/2)(ab+ba), clifford=Cl(9,0)_{T_a,T_b}=(1/2)delta_{ab}I,
%   octonion_basis=fano_e1e2=e4, complex_structure=u_equals_e7,
%   peirce_idempotent=E_{11}, real_form=E6(-26)

\documentclass[11pt]{article}
\usepackage{preamble}

\title{The Self-Modeling Basin Is Exceptional Supergravity}

\author{Bryan Ehrlich\\[4pt]
  \normalsize Independent researcher, Trumbull, Connecticut 06611, USA\\
  \normalsize ehrlich.bryan@gmail.com}
\date{}

\begin{document}

\maketitle

\begin{abstract}
The self-modeling framework identifies quantum mechanics with
faithful self-modeling: a finite-dimensional system that contains a
faithful model of itself necessarily has
$M_n(\mathbb{C})^{\mathrm{sa}}$ state spaces. A companion paper
identifies the exceptional Jordan algebra $\hthree$ as the unique
self-modeling basin, forced by non-composability. We show that the
algebraic data of $\hthree$ uniquely match the exceptional entry in
the Gunaydin-Sierra-Townsend (GST) classification of $N{=}2$
Maxwell-Einstein supergravity theories: within the GST
classification, the algebraic data of $\hthree$ uniquely select the
exceptional entry, whose bosonic Lagrangian includes the
Einstein-Hilbert term $-R/2$. An
observer at a rank-1 idempotent induces a Peirce decomposition
$27 = 1 \oplus 16 \oplus 10$. The $C^*$-bottleneck projects the
Peirce complement $\Vzero = \htwo{O}$ to
$\htwo{C}_u \cong \mathbb{R}^{3,1}$, yielding a 4-dimensional
algebraic Minkowski space with conformal algebra
$\mathfrak{so}(4,2)$. The unique $\Ffour$-invariant cubic form
$\det(X)$ on $\hthree$ (Springer uniqueness), which also governs
the self-modeling density $\rho_J$, serves as the gravitational
prepotential. The algebra $\hthree$ satisfies all three GST
hypotheses (degree~3, formally real, positive-definite trace form),
and the GST bijection uniquely identifies the algebraic data with
the exceptional $N{=}2$ Maxwell-Einstein supergravity in five
dimensions. The $r$-map (dimensional reduction) gives the
4-dimensional theory with scalar manifold
$\Eseven / (E_{6(-78)} \times \UU{1})$ and 28 vectors (27~matter
plus graviphoton), with all couplings determined by $\det(X)$.
The $N{=}2$ structure appears only as the \emph{output} of the
classification, not as an input. The result follows from two
inputs (the self-modeling definition and the identification of
$\hthree$ as the basin) plus the shared assumption that the
algebraic spacetime carries field-theoretic dynamics on a smooth
manifold.
\end{abstract}

\input{sections/introduction}
\input{sections/basin}
\input{sections/spacetime}
\input{sections/prepotential}
\input{sections/lagrangian}
\input{sections/discussion}

\section*{Acknowledgments}

AI language models (Claude, Anthropic) were used as interactive research
tools for mathematical exploration, literature search, and manuscript
drafting.  All derivations, proofs, and claims were conceived and verified
by the author.

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\bibliography{refs}

\end{document}
