\section*{Canonical diagnostics and baseline selection}

SFT uses a small set of diagnostics. The baseline measure is chosen by a single rule:

\begin{quote}
\textbf{Baseline selection rule.} If coupling constrains the image to a coupled subtorus coset $\mathrm{CST}_s$, the baseline is coupled Haar on $\mathrm{CST}_s$. Otherwise the baseline is Haar on the full torus.
\end{quote}

\begin{longtable}{@{}p{0.22\textwidth}p{0.54\textwidth}p{0.18\textwidth}@{}}
\toprule
\textbf{Diagnostic} & \textbf{Definition} & \textbf{Target} \\
\midrule
\endhead
Coverage profile (CP) &
$\mathrm{CP}(\rho)=\inf_{y}\,\mu(B_\rho(y))$ for the pushforward $\mu=\Phi_\#\nu$ and arc neighborhood $B_\rho(y)$ &
Haar on $T_P$ or coupled Haar on $\mathrm{CST}_s$ \\
Fourier uniformity defect (FUD) &
$\mathrm{FUD}_N=\sum_{1\le |n|\le N}|\widehat{p}(n)|$ for phase density $p$ on $\mathbb{T}_P$ &
Haar baseline (uncoupled) or free-coordinate Haar (coupled) \\
Spatial uniformity defect (SUD) &
distance of $\mu_s$ from the baseline measure in a chosen metric (TV or $L^2$ when available) &
baseline measure per rule above \\
\bottomrule
\end{longtable}

Rates and thresholds used with these diagnostics are centralized in \codeid{engine/contracts/constants_thresholds.md}.
