1\section{Ablations and falsification}2\label{sec:ablations}34Every variant in Table~\ref{tab:ablations_crps_scaled} is a Small model trained for \num{4000} steps with the same5seed and compared, on the 2024 development test, with a reference trained under exactly the same budget6(\textsc{mrpt-s}, 4k); two further seeds of the reference give the noise floor. Figure~\ref{fig:ablations_forest}7shows the relative CRPS changes at sixty minutes with their day-cluster intervals.89\input{tables/ablations_crps_scaled}1011\paragraph{Resolutions (H1 again).} At this shorter budget removing the 5- and 30-minute branches costs12$+0.12$ to $+0.16$\,\% of CRPS, removing only the 30-minute branch $+0.10$\,\%; the seed-to-seed spread of the13reference is $-0.03$ to $+0.16$\,\%. Multi-resolution context is therefore a real but marginal regulariser at small14budgets and, as Section~\ref{sec:results} showed, nothing at all at the full budget and out of sample.1516\paragraph{What the model actually uses.} The most informative ablations are the destructive ones. A model that17sees \emph{only} the calendar and missingness flags---no returns, no ranges, no volumes, just the trailing scale18$\sigma_t$ in its global token and the time of day---is worse than the full model by only $+0.20$ to $+0.29$\,\%.19Returns-only inputs cost $+0.19$ to $+0.28$\,\%; dropping relative volume $+0.08$ to $+0.14$\,\%; shuffling the order20of the 390 one-minute bars at training and evaluation time $+0.13$ to $+0.21$\,\%. In other words, of the21$\approx 4.3$\,\% improvement over the random walk at sixty minutes, roughly nine tenths come from the trailing22volatility level and the intraday seasonal, which every baseline also has, and at most three tenths of a percent23from any minute-level \emph{structure}---order, shape of bars, volume---that a sequence model can extract. The24falsification test passes in the sense intended: shuffling does hurt, so the model reads order; it just does not25have much to read.2627\paragraph{Fusion, head, regime (H3), identity.} Cross-attention fusion of separate per-scale encoders is slightly28worse than the shared backbone ($+0.05$\,\%). The Gaussian head is \IfFileExists{tables/ablations_gaussian_note.tex}{\input{tables/ablations_gaussian_note}\unskip.}{worse than the Student-$t$ head (see Table~\ref{tab:ablations_crps_scaled}).}29Removing the regime embedding changes nothing ($+0.02$ to $+0.03$\,\%, Holm $p>0.3$ at 30 and 60 minutes), and30coverage on stress days is identical with and without it (0.57/0.85/0.97 at $H=60$): Hypothesis~\ref{h3} is31rejected---the global token already carries the regime statistics, and conditioning the decoder on them again32adds nothing. A learned eight-code regime codebook improves CRPS by $0.03$--$0.15$\,\% and lowers central coverage33toward nominal (0.56 at 50\,\%), the only architectural change with a consistent, if small, benefit. A ticker-identity34embedding hurts ($+0.05$ to $+0.31$\,\%): instrument identity over-fits at this scale, which is also why the core model35has none.3637\paragraph{Joint paths (H4).} The copula head trained on the probability-integral transforms of the Stage-A38marginals converges to a copula log-likelihood of $-2.5\times10^{-5}$ per dimension, i.e.\ to independence, and39its loadings stay near zero. Correlated sampling changes the energy score by $-0.003$\,\%, the variogram score by40$-0.002$\,\%, the CRPS of maximum drawdown by $-0.01$\,\% and of realised variance by $+0.10$\,\%, all with intervals41containing zero (Table~\ref{tab:path_scores}); the CRPS of the cumulative return is $+0.08$\,\% worse at sixty42minutes. Hypothesis~\ref{h4} is rejected: once the marginals are conditioned on the recent history, the next sixty43minute returns are, to the resolution of these scores, conditionally independent, and a dependence-aware decoder44has nothing to model. We did not pursue diffusion decoders.4546\begin{figure}[htbp]\centering47\includegraphics[width=\textwidth]{figures/fig_ablations_forest.pdf}48\caption{Ablations at the Small scale (4 000 steps each): relative CRPS change at $H=60$ versus the random walk,49with 95\,\% day-cluster bootstrap intervals; the equal-budget reference and its two extra seeds are included.}50\label{fig:ablations_forest}51\end{figure}5253\begin{table}[htbp]\centering\small54\caption{Joint paths versus independent sampling of the same Student-$t$ marginals (MRPT-S + copula, 2024 development test, \num{986468} origins, 60-minute paths, 200 draws; day-cluster bootstrap 95\,\% intervals of the difference).}55\label{tab:path_scores}56\begin{tabular}{lccc}57\toprule58Score & Joint (copula) & Independent & Joint $-$ independent \\59\midrule60Energy score & 3.490e-3 & 3.490e-3 & $-9.2\times10^{-8}$ [$-2.3\times10^{-7}$, $+5.0\times10^{-8}$] \\61Variogram score ($p=0.5$) & 1.5113e-4 & 1.5114e-4 & $-3.8\times10^{-9}$ [$-1.0\times10^{-8}$, $+2.2\times10^{-9}$] \\62CRPS, maximum drawdown & 1.4632e-3 & 1.4633e-3 & $-1.8\times10^{-7}$ [$-6.2\times10^{-7}$, $+2.8\times10^{-7}$] \\63CRPS, realised variance & 1.1881e-5 & 1.1869e-5 & $+1.2\times10^{-8}$ [$-2.8\times10^{-9}$, $+3.0\times10^{-8}$] \\64\bottomrule65\end{tabular}66\end{table}67