Hypothesis~\ref{h2} asks whether pooled training transfers. On the sixty instruments never seen in training
(\num{250322} origins in 2024, Table~\ref{tab:main_crps_scaled_heldout}), MRPT-S improves on the random walk by
\pwmainheldoutmrptsmallvsnaiverwHfive{}\,\% at five minutes and \pwmainheldoutmrptsmallvsnaiverwHsixzero{}\,\%
at sixty, against \relmainmrptsmallcrpsHfive{}\,\% and \relmainmrptsmallcrpsHsixzero{}\,\% on the pooled instruments:
there is no transfer penalty. Against the baselines fitted on those same held-out instruments' own histories,
MRPT-S beats GARCH(1,1)-$t$ by 0.9--1.6\,\%, EWMA by 0.6--1.2\,\%, the TCN and the MLP by 0.1--0.4\,\%, HAR-RV by
\pwmainheldoutmrptsmallvsharrvHfive{}\,\% at five minutes, and is statistically tied with HAR-RV, ridge and
LightGBM from thirty minutes on (Holm-adjusted $p=1$). The multi-resolution gain over the one-minute-only twin is
again a tenth of a percent at most. Transfer therefore holds in the only sense the data support: a pooled model
without ticker identity forecasts unseen liquid instruments as well as it forecasts the instruments it was trained
on, and as well as---not better than---a heterogeneous variance regression refitted on the new instrument.

The untouched 2025 period (Table~\ref{tab:final_crps_scaled}; \num{1008425} pooled origins and \num{254334}
held-out origins, models and baselines frozen from the main study) repeats the 2024 picture almost line by line.
All models beat the random walk by 3.8--4.4\,\%; the neural models lead at five minutes
(\crpsfinalmrptsmallHfive{} against \crpsfinalharrvHfive{} for HAR-RV, \pwfinalmrptsmallvsharrvHfive{}\,\%);
HAR-RV, ridge and LightGBM lead from fifteen minutes on (\crpsfinalharrvHsixzero{} against
\crpsfinalmrptsmallHsixzero{}, \pwfinalmrptsmallvsharrvHsixzero{}\,\%, $t=\tpwfinalmrptsmallvsharrvHsixzero{}$). The
multi-resolution effect vanishes entirely out of sample: MRPT-S versus its one-minute-only twin is
\pwfinalmrptsmallvsmrptsmallonemonlyHfive{}\,\% at five minutes and \pwfinalmrptsmallvsmrptsmallonemonlyHsixzero{}\,\%
at sixty minutes (Holm $p=\ppwfinalmrptsmallvsmrptsmallonemonlyHsixzero{}$), and on the held-out instruments in 2025
every one of the four contrasts has $p=1$. Base and Small remain indistinguishable. One nuance appears on 2025
stress days (top decile of cross-sectional volatility, \num{101561} origins): HAR-RV's 50/80/95\,\% intervals cover
46/77/95\,\% of outcomes while MRPT-S covers 55/84/95\,\%; the regression's variance forecasts lag on the days
when volatility jumps, and the sequence model's wider body is, on those days, closer to the truth at 80\,\%, with the
same CRPS (0.4559 versus 0.4557 scaled).

\input{tables/main_crps_scaled_heldout}
\input{tables/final_crps_scaled}
\input{tables/final_calibration}