\section*{Classification program: target type and obstruction type}

SFT organizes cyclic phase-field systems by two coordinates:

\begin{itemize}[leftmargin=*]
\item \textbf{Target type:} full circle, full torus $T^k$, or coupled target $\mathrm{CST}_s$.
\item \textbf{Obstruction type:} one of the finite WOB classes when a witness cannot be certified.
\end{itemize}

\begin{longtable}{@{}p{0.24\textwidth}p{0.72\textwidth}@{}}
\toprule
\textbf{Class} & \textbf{Meaning in SFT} \\
\midrule
\endhead
Class A: forced full coverage & WSC exists on full circle or full torus; stability margins are recorded; diagnostics target Haar baseline. \\
Class B: forced coupled coverage & WSC exists on $\mathrm{CST}_s$; baseline is coupled Haar on $\mathrm{CST}_s$; convergence statements target coupled Haar. \\
Class C: embedded-only coverage & WSC exists on an embedded subsystem (loop/defect/orbit) even if global coverage is not claimed. \\
Class D: no forced coverage in declared regime & WOB exists; the obstruction code identifies why cyclic forcing cannot be certified in the declared measurement model. \\
\bottomrule
\end{longtable}

This classification is the ``periodic table'' of SFT: different-looking systems become the same object once the target type and obstruction type are identified.
