\begin{table}[htbp]\centering\small
\caption{H7 --- Validation of the region--category complexity indicator}\label{tab:h7}
\begin{tabular}{lr}\toprule
Validation statistic & Value \\\midrule
Matrix density (share of cells with RAA $\ge$ 1) & 0.409 \\
V1 ECI rank stability: median (p10) Spearman $\rho$, 500 store bootstraps & 0.20 (-0.54) \\
V1 Fitness / Diversity rank stability (median $\rho$) & 0.70 / 0.69 \\
V1 criterion ($\rho \ge 0.8$) for ECI & not met \\
V2 $\lambda_2$ of $\tilde M$: observed, null p95, $p$ & 0.252, 0.299, 0.414 \\
V2 spectral radius of the bipartite graph: observed, null p95, $p$ & 7.90, 8.79, 0.907 \\
V2 corr(ECI, diversity): observed, null [p5; p95] & 0.24, [-0.06; 0.57] \\
V4 Louvain communities: mode of count, median NMI across 200 seeds & 2, 1.0 \\
\bottomrule\end{tabular}
\begin{minipage}{0.95\textwidth}\vspace{2pt}\footnotesize\textit{Notes:} $M_{rc} = 1[\mathrm{RAA}_{rc} \ge 1]$ on merchant-equal weights, regional sample. Null = 2\,000 store-level region reshuffles. Per the preregistration, the ECI is reported as unstable when V1 fails and is omitted from the QDACI.\end{minipage}
\end{table}