\section*{Capstone theorem (COC \texorpdfstring{$\Rightarrow$}{=>} WSC/WOB, upgrades optional)}

\begin{theorem}[COC engine dichotomy]
Fix the declared hypothesis regime (including target type and perturbation model).
For every context in the Cyclic Observability Class (COC), the SFT engine outputs exactly one of the following:

\begin{itemize}[leftmargin=*]
\item a Witness Stability Certificate (WSC) asserting coverage on the correct target, with explicit margins and a validator predicate ledger, or
\item a Witness Obstruction (WOB) whose canonical code identifies the first failed validator predicate, together with evidence.
\end{itemize}

Moreover, any statistical or mixing statement is an \emph{optional upgrade}: it appears only when a convergence certificate is explicitly declared and its baseline matches the correct target.
\end{theorem}

This capstone statement is supported by the theorem schema templates (action and loop forcing), the predicate-exhaustion completeness lemmas, and the target-correctness axioms.

