\section{Robustness, falsification and failed tests}\label{sec:robust}

Table~\ref{tab:robust} collects the registered robustness checks on the H1 statistic. The median gap is 0.163 on the balanced panel of 1{,}300 groups present in all eleven weeks, 0.154 with unit-price normalisation, 0.151 after trimming the 1st and 99th percentiles (mean 0.181 against 0.189 untrimmed), 0.183 on cross-company group-weeks only, 0.135 when only non-promoted weeks are kept and 0.237 in group-weeks where at least one banner is promoted; across matching tiers (A, A+B, A+B+C, A+B+C+D) and posted-price definitions (mode, minimum, maximum, time-weighted mean) it ranges from 0.138 to 0.154, and adding circular listings leaves it at 0.154. Dispersion is therefore not an artefact of a tier, a price definition, outliers or promotions, although promotions widen it.
\input{tables/tab_robustness}

The category-level sign tests that the median gap exceeds 5\% reject for eight of eleven categories after Holm correction and do not reject for fresh produce, deli/cheese and ready meals. Table~\ref{tab:holm} applies Holm's correction across the primary tests: H1 (both criteria), H2, the H3 reference-change tests and the H4 lag-1 association remain significant; the market-level H5 gap does not.
\input{tables/tab_holm}

\paragraph{Falsification tests that passed.} The AR(1) placebo (permuted banner labels) returns 0.004; the H3 placebo at random dates returns $+0.0003$; single-store shops show 4.7\% multi-price weeks against 22.8\% in anti-bot feeds; the H4 leads for all-rival and same-company rivals are indistinguishable from zero.

\paragraph{Tests that failed or were inconclusive.} (i) The cross-company lead placebo in Model~C fails ($-0.108$, s.e.\ 0.048): with 1{,}784 observations and common weekly shocks, the descriptive lag coefficients for other-company rivals cannot be read as responses. (ii) The event-study pretrend test rejects; the decomposition by feed type attributes most of the pre-sale elevation to store-mixture noise, leaving a small exploratory residual. (iii) The market-level H5 gap is not different from zero over eleven weeks; the hypothesis holds only at the banner level. (iv) Tier~C matching failed validation (precision 0.42) and was removed from the primary specification; a first version of the matcher based on token-set similarity was rejected outright. (v) The preregistered basket rule left only seven items common to all wide-coverage banners and had to be amended (A-001). (vi) The comparison with Statistics Canada rests on two monthly observations and is inconclusive. We regard reporting these as part of the result.

\paragraph{Out-of-time validation.} Model~F's rolling-origin design is the only strictly out-of-time evidence in the paper; the promotion-state forecasts (AUC 0.94) are the component of the architecture that generalises forward within the window.