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%\includeonly{intro,Chap5}
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\title{Geometric Computation: Twin Helices and \\ the Algebra of Flow}

\author{Benjamin Kaminsky\footnote{benkaminskymath@gmail.com}}

\begin{document}
\maketitle

\begin{abstract}
This work constructs a manifold consisting of twin helices to investigate the existence of computational geometric bordisms, as part of the broader program of the Cobordism Hypothesis. We use these structures to define a class of deterministic computational substrates, termed \emph{Geometrically Computable Manifolds}, and study their geometric, algebraic, and computational properties. We show that, in a discrete regime, these manifolds encode arbitrary cyclic groups and support universal computation. This leads to a hypothesis describing the structural trade-offs in physical computation across distinct computational phases. We then analyze a regime in which abelian gauge computation is modeled with ordinary differential equations, linking the construction to continuous geometric dynamics. This signals a new research direction in physical mathematics at the intersection of geometry, gauge theory, and computability theory, termed \emph{Geometric Computability Theory}, in which computation is treated as a property of geometric compositions. This perspective opens avenues for future investigation, motivating the development of a constructive computational gauge theory with applications to Yang–Mills theory. As of this writing, no complete unified compositional semantics yet exists for the full range of these manifolds; future work will develop such a formalism.
\end{abstract}

\vspace{1em}

\noindent\textbf{Keywords:} geometric computation, higher gauge theory, prequantum geometry, Yang-Mills theory, cobordism hypothesis, helices, topological quantum field theory.

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\input{intro}
\input{Chap1}
\input{Chap2}
\input{Chap3}
\input{Chap4}
\input{Chap5}

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