\begin{table}[p]
\centering\scriptsize
\begin{threeparttable}
\caption{Monte Carlo, pois design, $p = 3$, $N = 65,536$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_pois_p3}
\begin{tabular}{@{}lrrrrrr@{}}
\toprule
Estimator & \multicolumn{3}{c}{$m = 32$, $K = 2,048$} & \multicolumn{3}{c}{$m = 64$, $K = 1,024$} \\
 & gap & RMSE & cov & gap & RMSE & cov \\
\midrule
(1,0) plain average & 10.480 & 10.623 & 0.581 & 5.054 & 5.276 & 0.629 \\
(1,1) average + 1 Newton & 0.222 & 1.592 & 0.949 & 0.051 & 1.595 & 0.953 \\
(1,2) average + 2 Newton & 1.03e-4 & 1.580 & 0.952 & 5.45e-6 & 1.593 & 0.954 \\
(2,0) half-block jackknife & 2.702 & 3.111 & 0.644 & 0.879 & 1.843 & 0.904 \\
(2,1) half-block + 1 Newton & 0.031 & 1.580 & 0.951 & 0.002 & 1.594 & 0.954 \\
(2,2) half-block + 2 Newton & 5.30e-5 & 1.580 & -- & 2.05e-8 & 1.593 & -- \\
(3,0) quarter-block & 1199.057 & 1199.047 & -- & 1.045 & 1.931 & -- \\
(3,1) quarter-block + 1 Newton & 1198.464 & 1198.453 & 0.348 & 0.007 & 1.594 & 0.954 \\
analytic Cox--Snell + 1 Newton & 0.001 & 1.580 & 0.952 & 6.26e-4 & 1.593 & 0.954 \\
CSL, 1 round & 3.362 & 3.712 & -- & 1.044 & 1.907 & -- \\
CSL, 2 rounds & 4.386 & 4.674 & -- & 0.645 & 1.735 & -- \\
AEE (Lin--Xi) & 10.100 & 10.198 & -- & 4.964 & 5.235 & -- \\
(2,1) stale Hessian & 0.036 & 1.580 & -- & 0.008 & 1.594 & -- \\
centralized MLE & 0 & 1.580 & 0.952 & 0 & 1.593 & 0.954 \\
\bottomrule
\end{tabular}
\begin{tablenotes}\footnotesize
\item 1000 paired replications per column. gap $=$ root mean square of $\sqrt N\,\lVert\tilde\theta - \widehat\theta_N\rVert$; RMSE $=$ root mean square of $\sqrt N\,\lVert\tilde\theta - \theta_0\rVert$; cov $=$ empirical coverage of nominal 95\% Wald intervals (observed information at the estimate; `--' when not computed). Monte Carlo standard errors of the gaps and RMSEs are in \texttt{results/processed/summary.csv}; coverage standard error $\approx 0.007$.
\item Fraction of workers with all local fits valid (orders 2 / 3): $m=64$: 1.000 / 1.000; $m=32$: 1.000 / 1.000.
\end{tablenotes}
\end{threeparttable}
\end{table}