% TARGET_DECISION_FLOW.tex

\clearpage
\section*{Target correctness decision flow}

This page is the canonical interface for selecting the \emph{correct target} and \emph{baseline} in SFT.
It is written to match the WSC schema fields \codeid{target_type} and \codeid{baseline}.
The point is simple: if the target is chosen correctly, the engine can attempt certification;
if the target is chosen incorrectly, the correct output is a named obstruction.

\medskip

\begingroup
\setlength{\tabcolsep}{4pt}
\small
\begin{longtable}{@{}p{0.32\linewidth}p{0.35\linewidth}p{0.27\linewidth}@{}}
\toprule
\textbf{Decision} & \textbf{Action (what you declare)} & \textbf{If violated, output}\\
\midrule
\endfirsthead
\toprule
\textbf{Decision} & \textbf{Action (what you declare)} & \textbf{If violated, output}\\
\midrule
\endhead

\textbf{A. Is the claim in \COC?}
& Declare a phase observable and an admissible witness route (rotation / loop-degree / holonomy / multi-cycle) and state the target rule you are using.
& If any ingredient is missing, the claim is outside \COC: boundary-type obstruction (typically \textbf{WOB-01}).\\

\textbf{B. Is coupling present?}
& If the model includes coupling constraints across phases (an integer constraint matrix $\chi$ or an equivalent coupling law), set
\codeid{target_type=CST} and declare \codeid{baseline=coupled Haar on CST}.
& Using circle/torus baseline under coupling, or failing to compute/declare CST: \textbf{WOB-06}.\\

\textbf{C. Single-cycle circle observable?}
& If the witness route is a circle action or a single loop/defect witness producing an integer $k\in\mathbb{Z}$, set
\codeid{target_type=circle} (or \codeid{embedded_circle} for subsystem-only claims) and \texttt{baseline=Haar on $\mathbb{T}_P$}.
& If every admissible witness integer is $0$: \textbf{WOB-02}. If no loop/orbit exists in the declared domain: \textbf{WOB-01}.\\

\textbf{D. Multi-cycle torus observable?}
& If the witness route is a $\mathbb{T}^k$ action with response map induced by an integer matrix $\chi$, compute the effective rank $r:=\mathrm{rank}(\chi)$.
\begin{itemize}[leftmargin=*]
\item If $r=k$, set \codeid{target_type=torus} and \texttt{baseline=Haar on $\mathbb{T}^k$}.
\item If $r<k$, set \codeid{target_type=subtorus_rank_r} and \texttt{baseline=Haar on the induced $r$-torus (the $\chi$-image)}.
\end{itemize}
& Claiming full-torus forcing when the response rank is deficient (or rational locking collapses the sweep): \textbf{WOB-10}.\\

\textbf{E. Target-aware upgrades?}
& Any convergence or mixing upgrade must explicitly name the baseline it converges to.
If the upgrade requires diffusion/mixing assumptions, record them and point to the declared evidence artifact.
& Mixing/convergence claimed without an admissible hypothesis package: \textbf{WOB-07}.\\

\bottomrule
\end{longtable}
\endgroup

\paragraph{Allowed upgrades (summary).}
\begin{center}
\begin{tabular}{@{}p{0.24\linewidth}p{0.33\linewidth}p{0.36\linewidth}@{}}
\toprule
\textbf{Target} & \textbf{Baseline} & \textbf{Upgrades allowed (when justified)}\\
\midrule
Circle / embedded circle & Haar on $\mathbb{T}_P$ & Stability margins (LCM/HMR), anti-collapse bounds, and convergence-to-Haar if a mixing model is declared.\\
Full torus $\mathbb{T}^k$ & Haar on $\mathbb{T}^k$ & Stability margins; rank-aware coverage; convergence-to-Haar if a mixing model is declared.\\
Subtorus rank $r$ & Haar on induced $r$-torus & Same upgrades, but always relative to the induced target (never the ambient torus unless $r=k$).\\
CST (coupled target) & Coupled Haar on CST & All upgrades, but always relative to coupled Haar; any non-coupled baseline is ill-posed (CTP/CHT).\\
\bottomrule
\end{tabular}
\end{center}
