1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\caption{Monte Carlo, pois design, $p = 8$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_pois_p8}5\begin{tabular}{@{}lrrrrrrrrrrrr@{}}6\toprule7Estimator & \multicolumn{3}{c}{$m = 64$, $K = 16,384$} & \multicolumn{3}{c}{$m = 128$, $K = 8,192$} & \multicolumn{3}{c}{$m = 512$, $K = 2,048$} & \multicolumn{3}{c}{$m = 1024$, $K = 1,024$} \\8 & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov \\9\midrule10(1,0) plain average & 53.236 & 53.275 & 0.354 & 25.472 & 25.627 & 0.777 & 6.187 & 6.617 & 0.829 & 3.082 & 3.988 & 0.845 \\11(1,1) average + 1 Newton & 1.433 & 2.892 & 0.917 & 0.322 & 2.570 & 0.948 & 0.019 & 2.493 & 0.951 & 0.005 & 2.514 & 0.949 \\12(1,2) average + 2 Newton & 0.001 & 2.502 & 0.952 & 5.19e-5 & 2.553 & 0.948 & 1.80e-7 & 2.493 & 0.951 & 1.15e-8 & 2.514 & 0.949 \\13(2,0) half-block jackknife & 14.549 & 14.784 & 0.065 & 3.503 & 4.334 & 0.732 & 0.612 & 2.575 & 0.944 & 0.406 & 2.545 & 0.946 \\14(2,1) half-block + 1 Newton & 0.108 & 2.506 & 0.951 & 0.006 & 2.553 & 0.948 & 2.22e-4 & 2.493 & 0.951 & 1.02e-4 & 2.514 & 0.949 \\15(2,2) half-block + 2 Newton & 6.53e-6 & 2.502 & -- & 2.13e-8 & 2.553 & -- & 4.59e-11 & 2.493 & -- & 9.93e-12 & 2.514 & -- \\16(3,0) quarter-block & 618.373 & 618.346 & -- & 1.891 & 3.191 & -- & 0.805 & 2.617 & -- & 0.568 & 2.575 & -- \\17(3,1) quarter-block + 1 Newton & 534.838 & 534.849 & 0.055 & 0.002 & 2.553 & 0.948 & 4.04e-4 & 2.493 & 0.951 & 2.01e-4 & 2.514 & 0.949 \\18analytic Cox--Snell + 1 Newton & 9.78e-4 & 2.502 & 0.952 & 4.10e-4 & 2.553 & 0.948 & 9.93e-5 & 2.493 & 0.951 & 4.91e-5 & 2.514 & 0.949 \\19CSL, 1 round & 25.196 & 25.304 & -- & 7.563 & 7.937 & -- & 0.845 & 2.631 & -- & 0.294 & 2.535 & -- \\20CSL, 2 rounds & 39.205 & 39.284 & -- & 5.394 & 6.013 & -- & 0.219 & 2.502 & -- & 0.048 & 2.514 & -- \\21AEE (Lin--Xi) & 51.852 & 51.933 & -- & 25.195 & 25.296 & -- & 6.159 & 6.697 & -- & 3.063 & 3.950 & -- \\22(2,1) stale Hessian & 0.063 & 2.502 & -- & 0.011 & 2.553 & -- & 9.31e-4 & 2.493 & -- & 3.32e-4 & 2.514 & -- \\23centralized MLE & 0 & 2.502 & 0.952 & 0 & 2.553 & 0.948 & 0 & 2.493 & 0.951 & 0 & 2.514 & 0.949 \\24\bottomrule25\end{tabular}26\begin{tablenotes}\footnotesize27\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 $\approx 0.007$.28\item Fraction of workers with all local fits valid (orders 2 / 3): $m=64$: 1.000 / 1.000; $m=128$: 1.000 / 1.000; $m=256$: 1.000 / 1.000; $m=512$: 1.000 / 1.000; $m=1024$: 1.000 / 1.000.29\end{tablenotes}30\end{threeparttable}31\end{table}32