trw-erb-sigc.tex

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\title{Terminal Rigidity Witnesses and the Einstein--Rosen Bridge:\\
A Zero-Capacity Invariant for Physical Inference}
\author{Inacio F. Vasquez\\Independent Researcher}
\date{January 2026}

\newtheorem{theorem}{Theorem}
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\newcommand{\Capacity}{\mathrm{Cap}}
\newcommand{\TC}{\mathrm{TC}}
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\begin{document}
\maketitle

\begin{abstract}
We formalize the notion of a \emph{Terminal Rigidity Witness}: a physical system whose global
structure is nontrivial while its operational information capacity is exactly zero.
We show that the classical Einstein--Rosen bridge provides a canonical example.
\end{abstract}

\section{Transcript Capacity}

For an interface producing transcript $Y_{1:T}$ from hidden state $X$, define
\[
\TC(T) := \sup I(X;Y_{1:T}).
\]

\section{Terminal Rigidity}

A system $S$ is a terminal rigidity witness if
\[
\Capacity(\mathcal C_S) = 0
\]
while $S$ has nontrivial global structure.

\section{Einstein--Rosen Bridge}

Topological censorship implies no causal curve connects the two asymptotic regions of the
maximal Schwarzschild extension. Hence the induced channel has zero capacity.

\begin{theorem}
The Einstein--Rosen bridge is a terminal rigidity witness.
\end{theorem}

\end{document}