1\section{Results}\label{sec:results}23All regional results use the regional sample (1{,}331 located stores, 298{,}362 listings) under the classifier labelling (primary, Amendment A-002); the preregistered rule labelling is reported in the same tables and in Section~\ref{sec:robust}. Figure~\ref{fig:map} shows coverage.45\begin{figure}[htbp]\centering6\includegraphics[width=\textwidth]{\FM{coverage_map.pdf}}7\caption{Coverage of the regional sample: stores per administrative region (left) and FSA-centroid locations of geocoded stores, size proportional to the square root of the catalogue (right). Official MRNF boundaries; the southern part of the province is shown. Source: Fabri-Ka research snapshot (2026-11-01), authors' computations.}\label{fig:map}8\end{figure}910\subsection{H3 --- Concentration: a long tail of merchants, a short head of listings}\label{sec:results_h3}11We begin with concentration because it conditions everything else. Among the 1{,}557 stores of the assortment sample the median catalogue has 35 listings, the 90th percentile 312 and the 99th 3{,}359; the largest has 24{,}104. The Gini coefficient of listings across stores is 0.849 (store-bootstrap 95\% interval 0.811--0.878), the top one per cent of stores hold 44\% of listings (0.33--0.53) and the top decile 79\% (0.73--0.84); both preregistered thresholds are exceeded with intervals entirely above them, and H3 is supported (Table~\ref{tab:h3}). The rank--size relation has a log--log slope of $-1.65$; a discrete power law fitted from $x_{\min}=165$ listings ($\alpha=1.93$, 288 stores in the tail, KS 0.028) is favoured over a log-normal on the same tail (Vuong $z=4.99$), although the comparison is approximate (Section~\ref{sec:discussion}). Within regions the Gini ranges from 0.52 (Côte-Nord, 16 stores) to 0.92 (Outaouais); the top decile of stores holds between 45\% and 95\% of a region's listings (Appendix~\ref{app:concentration}). Figure~\ref{fig:ranksize} shows the distribution.1213\TR{h3_concentration}1415\begin{figure}[htbp]\centering16\includegraphics[width=0.62\textwidth]{\FR{rank_size.pdf}}17\caption{Rank--size distribution of merchant catalogue sizes, 1{,}557 stores, 370{,}054 listings (assortment sample). Dashed line: $x_{\min}$ of the power-law fit. Source: Fabri-Ka research snapshot (2026-11-01).}\label{fig:ranksize}18\end{figure}1920\subsection{H1 --- Regional specialization is a property of merchants, not of listings}\label{sec:results_h1}21Table~\ref{tab:h1} reports Cramér's $V$ of the region$\times$category table against the merchant-reshuffle null. Under merchant-equal weights the observed $V$ is 0.111 against a null mean of 0.086 and a null 95th percentile of 0.093 ($p<0.001$; 1{,}331 stores, 17 regions, 20 categories): the merchants located in a region publish systematically different kinds of products from a random draw of Quebec merchants. The same holds when regions are compared by the number of \emph{stores} present in each category rather than by listings ($V=0.056$ against 0.045, $p<0.001$). Under listing weights the observed $V$ is larger in absolute terms (0.320) but so is the null (0.299, 95th percentile 0.344; $p=0.21$), and after trimming the one per cent largest stores $V$ equals the null mean (0.191 against 0.189, $p=0.45$). The preregistered criterion for H1 required significance under both the merchant-equal and the trimmed scheme; it is met under the first only, so H1 is \emph{partially supported}: specialization exists in the population of merchants and disappears once catalogue volumes are counted, because volumes are dominated by a few large stores whose location is, from the point of view of category composition, as good as random. Under the rule labelling the pattern is the same ($V=0.105$ against 0.075, $p<0.001$; trimmed $p=0.49$), and so it is in every robustness variant (Section~\ref{sec:robust}).2223\TM{h1_raa}2425Figure~\ref{fig:raa} and Table~\ref{tab:raa_top} show where the merchant-level specialization lies. Twelve of the 340 region--category cells have a revealed assortment advantage whose store-bootstrap interval lies above one, and 64 have an interval below one. The largest advantages are pets in Montérégie (RAA 2.9), outdoor and sport goods in Capitale-Nationale (2.9), chocolate in Outaouais (2.8), fashion in Gaspésie--Îles-de-la-Madeleine (2.7), jewellery (2.2), fashion (1.9) and children's goods (1.7) in Montréal, alcohol in Montérégie (1.8) and Estrie (1.8), maple in Estrie (1.8) and art in Capitale-Nationale (1.8). Under the rule labelling the leading cells are fashion in Gaspésie, industrial goods in Centre-du-Québec, meat and fish in Bas-Saint-Laurent and Mauricie, jewellery and coffee in Montréal and maple in Estrie; the two labellings agree on the Montréal fashion--jewellery cluster and on Estrie's maple and alcohol, and disagree where the classifier moves listings out of ``other'' and ``fine grocery''. Several of the large point estimates rest on few stores (the Gaspésie fashion cell is three stores), which the intervals make visible; the absences are more robust than the advantages: jewellery is significantly under-represented among the merchants of Gaspésie, Centre-du-Québec and Côte-Nord, meat, cheese and maple among those of Côte-Nord.2627\begin{figure}[htbp]\centering28\includegraphics[width=\textwidth]{\FM{raa_heatmap.pdf}}29\caption{Revealed assortment advantage by region and category, merchant-equal weights, classifier labelling, regional sample (1{,}331 stores). Dots mark cells whose store-bootstrap 95\% interval excludes 1. Source: Fabri-Ka research snapshot (2026-11-01).}\label{fig:raa}30\end{figure}3132\TM{raa_top}3334\subsection{H2 --- Diversity is narrow in range and unrelated to regional scale}\label{sec:results_h2}35Regional assortment diversity is high everywhere: the merchant-equal normalised entropy ranges from 0.74 (Côte-Nord) to 0.91 (Abitibi-Témiscamingue), i.e.\ effective category counts between 9 and 15.5 out of 20 (Table~\ref{tab:region_summary}, Figure~\ref{fig:diversity}). Rarefied to fifteen stores the range narrows to 0.73--0.89 and the ordering is only partly stable: Abitibi-Témiscamingue is highest under both labellings, Montréal, Côte-Nord, Laval and Gaspésie lowest under the classifier labelling, Mauricie and Estrie lowest under the rule labelling, and the draw intervals overlap for all but the extremes. Across the sixteen regions with at least fifteen stores, the Spearman correlation of rarefied diversity with log population is $0.00$ (95\% bootstrap interval $-0.63$ to $0.60$), with log business locations $0.00$ ($-0.64$; $0.62$), with disposable income $-0.02$ ($-0.53$; $0.51$) and with log density $-0.20$ ($-0.79$; $0.45$) (Table~\ref{tab:h2}); under the rule labelling the point estimates are negative for population and density ($-0.20$ and $-0.37$) and positive for income ($0.39$), all with intervals covering zero. H2 is \emph{inconclusive}: with sixteen units the data cannot distinguish a null from a moderate association in either direction. What the data do show is that the online assortments of located merchants are not markedly broader in the large urban regions than in the peripheral ones; if anything Montréal's merchants, dominated by fashion and jewellery designers, publish a narrower mix than those of Abitibi-Témiscamingue or Outaouais.3637\begin{figure}[htbp]\centering38\includegraphics[width=0.7\textwidth]{\FM{diversity_region.pdf}}39\caption{Regional assortment diversity under the classifier labelling: rarefied entropy (mean over 2{,}000 draws of fifteen stores, bars = 2.5--97.5 percentiles of the draws) and merchant-equal entropy on all stores; sixteen regions with at least fifteen stores. Source: Fabri-Ka research snapshot (2026-11-01).}\label{fig:diversity}40\end{figure}4142\TM{h2_scale}4344\subsection{H5 --- Matched products: dispersion by geography and by channel}\label{sec:results_h5}45The primary matched sample contains 2{,}203 listings in 1{,}064 groups sold by 143 stores in fifteen regions, nine of which have at least five matched stores (the preregistered threshold of eight is met). Within a group the posted price of the same product differs across merchants by a median of 4.7 log points and by 28.8 at the 90th percentile; 29\% of groups have identical prices everywhere and 49\% differ by more than five per cent (Figure~\ref{fig:gaps}). In the hedonic regression (Table~\ref{tab:h5}) the fourteen region effects are jointly significant under the wild cluster bootstrap (Wald 164.4, $p=0.0045$): T1 is supported. The individual region effects (Figure~\ref{fig:regeff}) are small and imprecise --- within $\pm0.08$ log points of Montréal for the regions with ten or more matched stores --- so the joint rejection says that regional price levels for identical goods are not all equal, not that any region is systematically expensive; with one store per region in Abitibi-Témiscamingue and Côte-Nord the effect is a single merchant's pricing. The channel effect is sharper: resellers and collective storefronts post prices $-0.116$ log points (cluster SE 0.027, wild-bootstrap $p=0.0012$) below producers' own shops for the same product, and certified stores $-0.073$ (SE 0.023); T2 is supported. Catalogue size has no effect (0.002, SE 0.008). Adding the fuzzy tier C (1{,}189 groups, 156 stores) leaves the conclusions unchanged (region $p=0.016$, reseller $-0.101$, $p=0.003$), and tier D --- identical titles across artisanal shops, 17\% of which are the same product --- shows median gaps of 26 log points, which is what different products look like.4647\TR{h5_hedonic}4849\begin{figure}[htbp]\centering50\includegraphics[width=\textwidth]{\FR{price_gaps.pdf}}51\caption{Left: within-group max--min log price gap for the 1{,}064 matched groups (tiers A+B, comparable variants, both stores located). Right: cumulative distribution of absolute log gaps of candidate pairs by tier. Posted prices at the snapshot. Source: Fabri-Ka research snapshot (2026-11-01).}\label{fig:gaps}52\end{figure}5354\begin{figure}[htbp]\centering55\includegraphics[width=0.7\textwidth]{\FR{h5_region_effects.pdf}}56\caption{Region effects on the log posted price of matched products relative to Montréal ($\pm1.96$ store-clustered SE; stores per region in parentheses). Identified only through groups spanning regions. Source: Fabri-Ka research snapshot (2026-11-01).}\label{fig:regeff}57\end{figure}5859\paragraph{A descriptive contrast that is not H6.} Across the whole price sample, within category, stores certified by Aliments du Québec or Les Produits du Québec post prices 0.20 log points below other stores (store-clustered SE 0.14; Table~\ref{tab:cert}). This is a store-level contrast between certified enterprises and others, confounded by category composition within the twenty bins and by store size; it says nothing about a premium for products made in Quebec, which cannot be identified in this source.6061\TR{cert_contrast}6263\subsection{H7 --- The complexity indicator does not survive validation}\label{sec:results_h7}64The binary region--category matrix ($M_{rc}=1$ if RAA $\ge1$, 40\% of cells) yields a diversity count, an ECI and a fitness index per region (Appendix~\ref{app:indicators}). Table~\ref{tab:h7} reports the validation. V1 fails: across 500 bootstrap resamples of stores the median Spearman correlation between the resampled and the full-sample ECI ranking is 0.67 (tenth percentile $-0.34$) against a criterion of 0.8; fitness (0.55) and even plain diversity (0.61) are also unstable, because with 17 regions and 20 categories the matrix is small and the marginal cells depend on a handful of merchants. V2 is mixed: the second eigenvalue of $\tilde M$ is larger than in all 2{,}000 merchant reshuffles ($p<0.001$) --- there is more block structure than chance --- but the spectral radius of the bipartite graph is not ($p=0.97$), and the ECI--diversity correlation (0.43) lies within the null band ($-0.09$; $0.57$). V3 fails: regressed on log population, log business locations and income the ECI has an $R^2$ of 0.25 and a leave-one-region-out predictive correlation of 0.00. Under the rule labelling V1 is worse (0.20) and V2 fails on both statistics. V4 is the only clean result: Louvain finds the same two communities in all 200 seeds (NMI 1.0), a food block (maple, fine grocery, chocolate, bakery, meat and fish, cheese, beverages, coffee and alcohol) and a non-food block (Figure~\ref{fig:network}); it is also the least informative, since it reproduces the obvious food/non-food divide. By the preregistered rule the indicator is reported as unstable, not called a complexity index, and excluded from the index family.6566\TM{h7_validation}6768\begin{figure}[htbp]\centering69\includegraphics[width=0.8\textwidth]{\FM{category_network.pdf}}70\caption{Category relatedness: maximum spanning tree (dark) and top-quintile proximity edges (light) of the Hidalgo-type proximity computed from co-occurrence of categories across stores; node colour = Louvain community. Source: Fabri-Ka research snapshot (2026-11-01).}\label{fig:network}71\end{figure}7273\begin{figure}[htbp]\centering74\includegraphics[width=\textwidth]{\FM{h7_validation.pdf}}75\caption{Left: ECI against diversity across the 17 regions. Right: rank stability of the three indicators under 500 store bootstraps; the preregistered criterion (median $\rho\ge0.8$) is not met. Source: Fabri-Ka research snapshot (2026-11-01).}\label{fig:h7}76\end{figure}7778\subsection{H4 --- Related diversification: a store-level association over ten weeks}\label{sec:results_h4}79After onboarding ended, 1{,}540 stores had 22{,}920 (store, category) cells absent in weeks 36--39; 104 of them (82 stores) acquired at least one listing in that category in weeks 40--44. Entries occur in categories whose relatedness density to the store's baseline portfolio is higher (0.33 against 0.25); the linear probability model with store and category fixed effects gives a density coefficient of 0.065 (store-clustered SE 0.019, $t=3.5$), above the 95th percentile of 200 category-relabelled placebos (0.042; placebo $p=0.01$). Under the rule labelling the coefficient is 0.111 (SE 0.050) with 149 entries (Table~\ref{tab:h4}, Figure~\ref{fig:h4}). Twelve per cent of entering stores show a connector-driven burst of additions in the outcome window, so part of the margin is catalogue onboarding rather than economic entry. At the region level only three category entries occurred, all in Nord-du-Québec's three stores; by the preregistered rule the region-level version is untestable. H4 is therefore an exploratory, store-level association consistent with the principle of relatedness \citep{hidalgo2018}, over ten weeks, with no causal reading.8081\TM{h4_dynamics}8283\begin{figure}[htbp]\centering84\includegraphics[width=0.62\textwidth]{\FM{h4_density.pdf}}85\caption{Exploratory: share of absent (store, category) cells with an entry in weeks 40--44 by decile of relatedness density at baseline. Source: Fabri-Ka research snapshot (2026-11-01).}\label{fig:h4}86\end{figure}8788\subsection{QDACI --- components, no composite}\label{sec:results_qdaci}89The Quebec Digital Assortment and Complexity Index family is reported as four validated components per region with bootstrap intervals (Appendix~\ref{app:indicators}): rarefied diversity, specialization (mean absolute log RAA), concentration (within-region Gini) and coverage (stores per 100{,}000 inhabitants), plus the matched-product region effect for the six regions with at least ten matched stores; the complexity component is omitted. The three composite weightings disagree: the equal-weight and Borda rankings coincide by construction, but the first principal component (45\% of variance, loading negatively on diversity and positively on specialization and concentration) correlates with them at $\rho=0.25$ only, and the equal-weight ranking has a median bootstrap rank correlation of 0.47 with itself across store resamples. By the preregistered rule (median agreement $\ge0.7$) no composite is published. The components themselves say something coherent: the regions with the broadest and least specialised merchant populations (Abitibi-Témiscamingue, Laurentides, Outaouais, Bas-Saint-Laurent) are not the largest ones, and the regions with the highest coverage per inhabitant (Saguenay--Lac-Saint-Jean, Gaspésie, Estrie) are those served by regional agri-food directories --- a discovery effect, not an economic one.90