\section{Introduction}
\label{sec:introduction}

Every minute of a U.S. trading day leaves behind one bar---open, high, low, close, volume---for each of several
thousand instruments. Foundation models for time series promise to learn ``universal'' representations from such
streams and to forecast any series zero-shot \citep{ansari2024chronos, das2024timesfm}, and a growing literature
applies deep sequence models to intraday prices \citep{sirignano2019universal, zhang2019deeplob, kolm2023deep}.
Whether a compact model that reads several resolutions of minute-level history improves \emph{calibrated}
forecasts of the next hour, relative to the simplest volatility models an econometrician would write down, is
however an empirical question that is rarely posed with matched information sets, proper scoring rules and
dependence-aware inference. This paper poses it narrowly and answers it on data.

We build CHRONOS-X, a research package around a Multi-Resolution Patch Transformer (\MRPT{}). At a decision time
inside the regular session the model reads the last 390 completed one-minute bars, the last five days of completed
5-minute aggregates and the last twenty days of 30-minute aggregates, each tokenised in patches with gated feature
projections, resolution and temporal-gap embeddings; a shared pre-norm Transformer encoder and a direct decoder
with sixty future-calendar queries emit a Student-$t$ marginal for each of the next sixty minute returns, and a
second-stage low-rank Gaussian copula turns the marginals into coherent sample paths. All inputs are strictly
causal, scale-free (divided by a trailing volatility computed at the origin) and masked where the source has no
bar; the model carries no ticker identity. Five hypotheses were written before any tuning: multi-resolution history
helps at equal parameters (H1), pooled training transfers to unseen instruments (H2), history-only regime
conditioning improves calibration under stress (H3), coherent paths beat independent marginals on path scores
(H4), and---exploratory---the forecasts carry economic content after costs (H5).

The data are 300 U.S. stocks and ETFs selected point-in-time at the end of 2017, stratified by asset class, dollar
volume, volatility and sector, with sixty instruments held out entirely; \num{234} million one-minute bars from a
private FirstRate Data lakehouse (FinData~OS) over 2018--2025, audited for timestamp conventions, session
boundaries, early closes, daylight-saving time, missing minutes, splits and dividends. Training uses 2018--2022,
validation 2023, the development test 2024 and an untouched final period 2025; evaluation uses \num{986468}
origins in 2024 alone. Baselines share the information set exactly: random walk, seasonal volatility, EWMA,
HAR-RV at the minute scale, GARCH(1,1)-$t$, ridge, elastic net, LightGBM, an MLP and a TCN with the same Student-$t$
head, and the one-minute-only \MRPT{} as the equal-parameter patch-Transformer control. Scores are the CRPS, the
weighted interval score, quantile losses, coverage, PIT diagnostics, QLIKE, tail Brier scores and, for paths,
energy and variogram scores; inference clusters by trading day and uses overlap-aware HAC Diebold--Mariano
statistics with multiple-testing control, because a million overlapping windows are not a million observations.

The answer is precise and mostly negative for the architecture, and informative about the data. Every model beats
the random walk by 3.5--4.9\,\% in CRPS at every horizon: the minute stream carries real information about the
dispersion of the next hour, and none about its direction (directional accuracy 0.50, median magnitudes below one
basis point, no economic content after costs; H5 rejected). The sequence models are the best at five minutes;
from fifteen minutes on, a heterogeneous autoregression of realised variance with a kurtosis-matched Student-$t$
is both sharper and better calibrated than any neural model, by 0.3--0.7\,\%. The multi-resolution context that
defines \MRPT{} improves on the one-minute-only twin by at most a tenth of a percent---statistically detectable on a
million origins, economically nil (H1 rejected in substance); a 20.7-million-parameter model does no better than a
3.5-million one. The remaining hypotheses are examined in the same spirit in Sections~\ref{sec:results}
and~\ref{sec:ablations}: zero-shot transfer to the sixty held-out instruments, regime conditioning on stress days,
the copula paths against independent sampling, and the untouched 2025 period.

The contribution is therefore a replicable measurement rather than a new state of the art: a documented data
pipeline and evaluation protocol for minute-level probabilistic forecasting under a private-use license, a compact
model that is competitive without being superior, and a set of null results that a reader can reproduce from the
released code and synthetic fixtures. Section~\ref{sec:hypotheses} states the hypotheses, Section~\ref{sec:literature}
places them in the literature, Sections~\ref{sec:data}--\ref{sec:design} describe data, model and design,
Sections~\ref{sec:results}--\ref{sec:ablations} report the results, and Sections~\ref{sec:limitations}--\ref{sec:conclusion}
discuss limitations, reproducibility and what the evidence does and does not say.