\section{Research question and falsifiable hypotheses}
\label{sec:hypotheses}

The question is narrow on purpose. At a decision time $t$ inside the regular session, with every one-minute bar up to
$t$ complete, can a compact model that reads the recent minute-level history \emph{and} coarser past-only aggregates
produce better-calibrated and sharper predictive distributions for the next $H\in\{5,15,30,60\}$ minutes than models
that only read the minute stream, or than well-specified non-neural volatility models? ``Better'' is defined by
strictly proper scoring rules \citep{gneiting2007strictly, matheson1976scoring}, never by price-level errors: on a
one-minute grid the random walk is a formidable point forecaster, and a model can look impressive on price-level
mean squared error while learning nothing \citep{cont2001empirical}. We therefore train and score on return-based
targets and evaluate full predictive distributions.

Let $r_{t+h}$ denote the log return of the bar opening $h$ minutes after $t$ and $R_{t,H}=\sum_{h\le H} r_{t+h}$
the cumulative return. The model emits, for each future minute, a Student-$t$ marginal with location, scale and
degrees of freedom, and (in a second stage) a dependence structure across the $H$ minutes. Five hypotheses were
written before any model was tuned and are tested as stated.

\begin{hypothesis}[Multi-resolution history]\label{h1}
At equal parameter count and training budget, a model whose encoder reads the last 390 one-minute bars, the last five
days of 5-minute aggregates and the last twenty days of 30-minute aggregates achieves a lower $\CRPS$ (and $\WIS$) for
$R_{t,H}$ than the same architecture reading the one-minute bars only.
\end{hypothesis}

\begin{hypothesis}[Transfer to unseen instruments]\label{h2}
A model trained on a pool of instruments, without any ticker identity, scores better on instruments it has never
seen than non-neural baselines fitted with the same information set, and its loss on unseen instruments is not
materially worse than on pooled instruments.
\end{hypothesis}

\begin{hypothesis}[History-only regime conditioning]\label{h3}
Conditioning the decoder on history-only regime statistics (trailing volatility and relative volume) improves
calibration---measured by coverage gaps and the probability-integral-transform (PIT) dispersion---on days whose
cross-sectional volatility is in the top decile, relative to the same model without regime conditioning.
\end{hypothesis}

\begin{hypothesis}[Coherent joint paths]\label{h4}
A dependence-aware decoder (a Gaussian copula with a low-rank factor structure over the $H$ future minutes, with the
Stage-A marginals held fixed) achieves lower energy and variogram scores for the joint path, and lower $\CRPS$ for
path functionals (maximum drawdown, realised variance), than sampling the same marginals independently.
\end{hypothesis}

\begin{hypothesis}[Economic content, exploratory]\label{h5}
Signals derived from the predictive median contain incremental information after an assumed round-trip cost; this
hypothesis is exploratory because no quote data are available and costs are assumptions.
\end{hypothesis}

Each hypothesis has a pre-specified test: a Diebold--Mariano statistic on the loss differential with an
overlap-aware heteroskedasticity- and autocorrelation-consistent variance \citep{diebold1995comparing,
harvey1997testing, newey1987simple}, a trading-day cluster bootstrap for interval estimates (all instruments of one
day form one cluster, because millions of overlapping windows are not independent observations), and Holm and
Benjamini--Hochberg adjustments across horizons and comparisons \citep{holm1979simple, benjamini1995controlling}.
Null findings are reported as such.