1\section{Robustness, alternative specifications and external validation}\label{sec:robust}23\subsection{Preregistered variants}4Table~\ref{tab:h1} (lower panel) and Figure~\ref{fig:robust} recompute the H1 statistics on the nine preregistered variants under the classifier labelling: the platform-label-first region assignment (1{,}214 stores), stores discovered through certification and association sources only (1{,}068), excluding Montréal (1{,}094), excluding the one per cent largest stores (1{,}318), eight macro-categories, dropping ``other'', excluding resellers and collective storefronts (1{,}306), and dropping the 30 stores whose region sources conflict (1{,}301). The merchant-equal result holds everywhere ($V$ between 0.106 and 0.121; permutation $p\le0.009$ in every variant), and the trimmed-listing result is never significant ($p$ between 0.07 and 0.76). The same is true under the rule labelling ($p\le0.006$ merchant-equal, $p\ge0.29$ trimmed). A hundred reassignments of categories drawn from the audit confusion matrix (rule labels perturbed cell by cell) keep the merchant-equal $V$ between 0.093 and 0.112 and reject the null in 82\% (classifier) and 88\% (rule) of draws. The Gini of catalogue sizes stays between 0.76 (without the largest one per cent) and 0.87 (without Montréal). The regional diversity ordering, by contrast, is labelling-sensitive beyond its extremes (Section~\ref{sec:results_h2}): we report it as an interval statement, not a league table.56\begin{figure}[htbp]\centering7\includegraphics[width=0.85\textwidth]{\FM{robustness_h1.pdf}}8\caption{H1 across preregistered sample and category variants, classifier labelling: observed Cramér's $V$ against the mean of the merchant-reshuffle null under merchant-equal (M) and trimmed-listing (T) weights. Source: Fabri-Ka research snapshot (2026-11-01).}\label{fig:robust}9\end{figure}1011\subsection{Price dispersion}12The H5 conclusions are unchanged with the fuzzy tier C (Table~\ref{tab:h5}), and the reseller effect is the single most stable estimate in the paper ($-0.10$ to $-0.12$ across specifications, wild-bootstrap $p\le0.003$). Two limits remain. Region effects for regions with one to three matched stores are individual merchants' pricing, and the joint test is driven by the nine regions with at least five matched stores; and because matching precision is 0.90--0.92, roughly one group in ten pairs different products, which inflates measured gaps --- the 29\% of groups with identical prices and the 4.7-point median are therefore upper bounds on dispersion among truly identical products in this sample, while the reseller contrast, estimated within group, is attenuated rather than inflated by false matches.1314\subsection{Holdouts}15Leave-one-region-out recomputation of the H2 correlations never moves the rarefied-diversity--population correlation outside $[-0.3, 0.3]$ under either labelling; the H7 leave-one-region-out predictive correlation is the V3 statistic reported above. The H4 temporal holdout (density from weeks 36--39, entries in 40--44) is built into the design. Duplicate products cannot leak between training and test in the classifier because the audit sample's identifiers were removed from the training sample before annotation; the embedding model saw all listings but was never fitted to labels.1617\subsection{External validation and selection}18Fabri-Ka's store counts per region correlate at 0.91 with ISQ business locations, 0.89 with retail locations, 0.93 with manufacturing locations and 0.84 with population (Spearman, 17 regions; Table~\ref{tab:external}), so the aggregator reproduces the size ordering of regional economies. Coverage is nonetheless uneven: from 1.8 stores per thousand business locations in Laval and 3.4 in Montréal to 9.0 in Estrie and 11.1 in Saguenay--Lac-Saint-Jean, a six-fold range, with the regions of high coverage being exactly those with a connected regional agri-food directory (Zone boréale, Créateurs de saveurs, Gaspésie gourmande). The 226 stores without a recoverable location come predominantly from a gift directory and from search sweeps, i.e.\ from the sources whose records carry no address. Discovery source and e-commerce platform mixes differ by region (Shopify dominates in Montréal and Laval, WooCommerce in the agri-food regions), and category mix differs by platform, so a platform-connector failure would be region-correlated; the trimmed, certification-only and no-Montréal variants are the operational answer to this threat and do not change the qualitative results. We have no regional measure of e-commerce adoption to weight by, and we do not attempt selection weights: the coverage ratios are reported so that readers can see where the merchant population is thinly or thickly observed.19