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. Every statistic in this section was recomputed after the three referee reports summarised in Appendix~\ref{app:prereg}; where a correction changed a conclusion we say so.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); points in the same FSA are stacked. Official MRNF boundaries; the southern part of the province is shown. Source: Fabri-Ka research snapshot (2026-11-01), author's 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) describes the tail, but it is not distinguishable from a log-normal fitted by maximum likelihood on the same truncated tail: the Vuong statistic is $-1.98$ in favour of the log-normal, whose fitted shape is degenerate (a very wide log-normal that mimics a power law), so we report the tail as heavy without naming its family --- a first draft's ``power law favoured'' rested on an untruncated log-normal fit and was withdrawn after refereeing. 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: 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 0.112 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 ($V=0.056$ against 0.045, $p<0.001$), at the level of the 56 MRCs with at least five geocoded stores ($V=0.185$ against 0.156, $p<0.001$), and --- the variant that matters most given how the platform discovers merchants --- when every store found through a region-specific directory is dropped (1{,}012 stores, $V=0.120$ against 0.098, $p<0.001$). Under listing weights the observed $V$ is larger in absolute terms (0.321) but so is the null (0.299, 95th percentile 0.344; $p=0.20$), and after trimming the one per cent largest stores $V$ equals the null mean (0.191 against 0.189, $p=0.43$). The preregistered criterion for H1 required significance under both the merchant-equal and the trimmed scheme; it is met under the first only, so by the rule we fixed in advance \textbf{H1 is not supported}, and the merchant-level dependence is reported as a descriptive finding outside the confirmatory family. Two qualifications apply. The listing-weighted null is a low-power comparison: the standard deviation of $V$ under the merchant reshuffle is six times larger under listing weights than under merchant-equal weights because four stores hold a quarter of the regional sample's listings, so the null cannot be rejected but neither is a listing-level effect excluded; and under the platform-label-only region assignment the listing-weighted statistic is significant ($p=0.024$), so the listing-level conclusion depends on where three recovered mega-catalogues are placed. 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 66 have an interval below one; these counts carry no multiplicity control, so we calibrated them against the merchant-reshuffle null, under which 2.9 cells (at most 8 in 20 permutations) exceed one and 55.5 (at most 69) fall below one. The excess of advantages is therefore modest and real, while the number of apparent absences is what the null produces on its own --- the opposite of what a reader of the raw counts would conclude. The largest advantages are pets in Montérégie (RAA 3.1), 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 (1.8) and maple (1.7) in Estrie, alcohol in Montérégie (1.8) and art in Capitale-Nationale (1.8). Several of these cells coincide with a region-specific discovery directory --- the Charlevoix route feeds 29 of the 66 art merchants and 9 of the 20 outdoor merchants of Capitale-Nationale, and Créateurs de saveurs 18 of the 47 maple merchants of Estrie --- and the merchant-reshuffle null does not absorb discovery selection; the province-wide-sources variant above shows that the aggregate dependence survives, but individual cells can be directory artefacts. 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 and alcohol in Estrie; the two labellings agree on Montréal's fashion--jewellery cluster and on Estrie, and disagree where the classifier moves listings out of ``other'' and ``fine grocery''. Point estimates built on few stores (the Gaspésie fashion cell is three stores) are flagged by their intervals.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 (no multiplicity control; see the text for the null-calibrated counts). Source: Fabri-Ka research snapshot (2026-11-01).}\label{fig:raa}30\end{figure}3132\TM{raa_top}3334\subsection{H2 --- Diversity: total variety rises with scale, per-merchant breadth does not}\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}). Two questions must be kept apart. The preregistered one --- is the breadth of a \emph{typical set of merchants} larger in larger regions --- is answered by the rarefied entropy (fifteen stores): its range is 0.73--0.89, its ordering is only partly stable across labellings (Abitibi-Témiscamingue is highest under both; Montréal, Côte-Nord, Laval and Gaspésie are lowest under the classifier labelling, Mauricie and Estrie under the rule labelling), and across the sixteen regions with at least fifteen stores its Spearman correlation with log population is $0.04$ (95\% interval, combining region and rarefaction resampling, $-0.65$ to $0.62$), with log business locations $0.04$, with disposable income $0.00$ and with log density $-0.15$ (Table~\ref{tab:h2}); with $n=16$ only $|\rho|\gtrsim0.66$ is detectable with 80\% power, so H2 is \emph{inconclusive}. The other question --- does the \emph{total} online variety of a region scale with its size, as business-type diversity does in the urban-scaling literature \citep{youn2016,hong2020} --- gets a different answer: the unrarefied merchant-equal entropy correlates at 0.52 with log population, 0.53 with business locations and 0.53 with income (intervals $-0.05$ to $0.92$), because more merchants fill more categories. Diversity rises with the number of located merchants; conditional on merchant count it shows no detectable association with scale.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 channel, not demonstrably by geography}\label{sec:results_h5}45The primary matched sample contains 2{,}203 listings in 1{,}064 groups (920 spanning at least two regions) sold by 143 stores in fifteen regions, nine of which have at least five matched stores (the preregistered threshold of eight is met). Its composition matters: 26\% of listings are health and beauty products, 24\% fine grocery and 15\% coffee and tea; 64\% of groups contain a reseller or collective storefront; and three natural-food resellers hold 38\% of the listings. 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 have a Wald statistic of 164, but the wild cluster bootstrap --- with the bootstrap disturbance re-projected off the group fixed effects, a correction made after refereeing that moved the $p$-value from 0.005 to 0.098 --- does not reject equality of regional price levels at conventional levels: \textbf{T1 is not supported}. The decomposition explains why the Wald statistic is large: Outaouais alone contributes 65 of the 164 (five matched stores, 84 of whose 110 listings belong to one bulk-food retailer), and without it the joint statistic falls to 51 on 13 degrees of freedom. The individual region effects (Figure~\ref{fig:regeff}) are within $\pm0.08$ log points of Montréal for the regions with ten or more matched stores. The channel effect is sharper and survives every correction: resellers and collective storefronts post prices $-0.116$ log points (cluster SE 0.027, wild-bootstrap $p=0.004$, Holm-adjusted 0.016) below producers' own shops for the same product, and certified stores $-0.072$ (SE 0.023); \textbf{T2 is supported}. Catalogue size has no effect (0.001, SE 0.008). Adding the fuzzy tier C (1{,}189 groups, 156 stores) leaves the channel result unchanged ($-0.101$, $p=0.017$) and makes the geographic test weaker still ($p=0.41$). Tier D --- identical titles across artisanal shops, 21\% of which are the same product --- shows median gaps of 26 log points, which is what different products look like. Because matching precision is 0.98--1.00 for tiers A and B, the measured gaps are not inflated by false matches to any material degree.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; the joint test does not reject equality (wild cluster bootstrap $p=0.098$). 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 0.68 (tenth percentile $-0.32$) against a criterion of 0.8; fitness (0.64) and plain diversity (0.64) 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 and therefore fails as a whole: 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 ($p=0.94$), and the ECI--diversity correlation (0.45) 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 0.26 and a leave-one-region-out predictive correlation of 0.01. Under the rule labelling V1 is worse (0.27) and both V2 statistics fail. V4 is the only clean result: Louvain finds the same two communities in all 200 seeds (NMI 1.0), a food block 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}79The dynamic exercise uses all 461{,}011 published listings of the 1{,}554 eligible stores, including the 71{,}722 that were no longer active at the snapshot (a first draft had used surviving listings only). After onboarding ended, stores had 22{,}263 (store, category) cells absent in weeks 36--39; 151 of them (98 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; the linear probability model with store and category fixed effects gives a density coefficient of 0.102 (store-clustered SE 0.031, $t=3.3$), above the 95th percentile of 200 category-relabelled placebos (0.051; placebo $p=0.005$). Under the rule labelling the coefficient is 0.093 (SE 0.054, placebo $p=0.055$) with 153 entries (Table~\ref{tab:h4}, Figure~\ref{fig:h4}). Nineteen 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 one category entry and no exit occurred in the window; 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, labelling-sensitive in its strength, 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 index family keeps the name under which it was preregistered (Quebec Digital Assortment and Complexity Index) although its complexity component is withheld. It 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 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 $\rho=0.29$ only, and the equal-weight ranking has a median bootstrap rank correlation of 0.45 with itself across store resamples. By the preregistered rule (median agreement $\ge0.7$) no composite is published. The components say something coherent: the regions with the broadest and least specialised merchant populations (Abitibi-Témiscamingue, Outaouais, Bas-Saint-Laurent, Laurentides) 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