\section{Exact finite assurance and reproducibility}
\label{sec:validation}

The proof above is deductive and alphabet-general.  The public executable
capsule is deliberately restricted to the binary specialization: it
reconstructs $k=2,4,6,8,10,12$ using exact cyclotomic
coordinates, verifies one-per-PCR selection, residual acyclicity, the
edgewise coboundary, every legal firing, and the final literal symmetry.
Keeping this scope explicit avoids presenting a finite sample as evidence for
an all-order or alphabet-general quantifier.

Two implementations are used.  The producer represents exact coordinates in
the appropriate quadratic or cyclotomic integer rings and uses Kahn's
algorithm for the residual DAG.  The independent validator uses frozen exact
coordinate tables and a recursive DFS DAG oracle; it does not import the
producer.  Both reconstruct the complete scientific payload rather than
comparing only summary counts.

The panel reports six rows and 612 legal source firings.  Seven scientific
mutations alter rotation, gradient, half-plane, ray, zero-tie, paired-update,
or firing conventions; seven independent envelope mutations alter retained
scientific fields.  Every mutation must be rejected.  Appendix
\ref{app:finite} gives the finite table, and the repository documentation
gives the exact replay commands and stable payload identity.

This executable layer neither implements the direct $q$-ary membership
algorithm of Corollary~\ref{cor:complexity} nor tests genomic data.  Those
absences are intentional: the repository accompanies a mathematical article,
not a sequence-analysis software release.