\chapter{Executable reference implementation}
\section{Core library}
The following is the complete library distributed as \texttt{aeqoria.py}.
Inputs are ordinary real matrix arrays and the declared normalized geometric
parameters. The code performs no network requests and requires no private
files. The functions are reference implementations rather than a specialized
large-scale numerical package.
\lstinputlisting[language=Python]{aeqoria.py}

\section{Complete verification driver}
The following driver is the source of the recorded 142 checks. Random trials
use a fixed seed. Each \texttt{record} call corresponds to one declared check;
a check can contain several related residual conditions, so the aggregate
count is not a count of independent mathematical theorems.
\lstinputlisting[language=Python]{verify_aeqoria.py}

\section{High-precision example generator}
The table generator evaluates the explicit circle design. Its integer
ceilings are illustrative high-precision evaluations, not outward-rounded
certificates of global finite-length optima.
\lstinputlisting[language=Python]{create_examples.py}