1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\caption{Monte Carlo, logit design, $p = 3$, $N = 262,144$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_logit_p3}5\begin{tabular}{@{}lrrrrrr@{}}6\toprule7Estimator & \multicolumn{3}{c}{$m = 128$, $K = 2,048$} & \multicolumn{3}{c}{$m = 256$, $K = 1,024$} \\8 & gap & RMSE & cov & gap & RMSE & cov \\9\midrule10(1,0) plain average & 14.498 & 14.992 & 0.175 & 7.074 & 8.186 & 0.560 \\11(1,1) average + 1 Newton & 0.159 & 3.821 & 0.948 & 0.038 & 3.882 & 0.947 \\12(1,2) average + 2 Newton & 1.89e-5 & 3.819 & 0.948 & 1.07e-6 & 3.883 & 0.946 \\13(2,0) half-block jackknife & 2.142 & 4.359 & 0.908 & 0.814 & 3.967 & 0.939 \\14(2,1) half-block + 1 Newton & 0.004 & 3.819 & 0.948 & 5.65e-4 & 3.883 & 0.946 \\15(2,2) half-block + 2 Newton & 1.81e-8 & 3.819 & -- & 6.37e-10 & 3.883 & -- \\16(3,0) quarter-block & 28.168 & 28.417 & -- & 1.033 & 4.049 & -- \\17(3,1) quarter-block + 1 Newton & 10.997 & 11.618 & 0.938 & 8.19e-4 & 3.883 & 0.946 \\18analytic Cox--Snell + 1 Newton & 3.44e-4 & 3.819 & 0.948 & 1.93e-4 & 3.883 & 0.946 \\19CSL, 1 round & 2.120 & 4.408 & -- & 0.710 & 3.937 & -- \\20CSL, 2 rounds & 0.596 & 3.849 & -- & 0.127 & 3.888 & -- \\21AEE (Lin--Xi) & 13.417 & 13.951 & -- & 6.794 & 7.708 & -- \\22(2,1) stale Hessian & 0.060 & 3.820 & -- & 0.012 & 3.883 & -- \\23centralized MLE & 0 & 3.819 & 0.948 & 0 & 3.883 & 0.946 \\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): $m=256$: 1.000 / 1.000; $m=128$: 1.000 / 1.000.29\end{tablenotes}30\end{threeparttable}31\end{table}32