\begin{table*}[ht]
\centering
\caption{Summary of $H_0$ constraints. Fisher rows give the direct nearby-population result ($^\star$) or full-volume extrapolated values. Bayesian rows are blank for manual completion. Cells show mean\,$\pm$\,population scatter (MC error).}
\label{tab:sigma_H0_summary}
\begin{tabular}{lllccc}
\toprule
Detector & Approx. & Source & \multicolumn{3}{c}{$\sigma_{H_0}$ [km\,s$^{-1}$\,Mpc$^{-1}$]} \\
\cmidrule(r){1-3}\cmidrule(lr){4-6}
 &  &  & $N_{\mathrm{near}}$ & $N_{\mathrm{lo}}$ & $N_{\mathrm{hi}}$ \\
\midrule
\multicolumn{6}{l}{\textit{aLIGO/Virgo}} \\
 & MWM & Fisher & -- & 96.1 $\pm$ 33.4 (10.6) & 58.8 $\pm$ 20.4 (6.5) \\
 & MWM$^\dagger$ & Fisher & -- & 95.2 $\pm$ 33.2 (10.5) & 58.3 $\pm$ 20.3 (6.4) \\
 & NRSur & Fisher & -- & 91.8 $\pm$ 21.6 (6.8) & 56.2 $\pm$ 13.3 (4.2) \\
 & MWM & Fisher$^\star$ & 398.8 $\pm$ 32.4 (10.2)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{ET}} \\
 & MWM & Fisher & -- & 1.70 $\pm$ 0.33 (0.10) & 0.984 $\pm$ 0.191 (0.061) \\
 & MWM$^\dagger$ & Fisher & -- & 1.70 $\pm$ 0.32 (0.10) & 0.979 $\pm$ 0.187 (0.059) \\
 & NRSur & Fisher & -- & 1.61 $\pm$ 0.27 (0.09) & 0.931 $\pm$ 0.158 (0.050) \\
 & MWM & Fisher$^\star$ & 26.1 $\pm$ 1.6 (0.5)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{CE}} \\
 & MWM & Fisher & -- & 1.06 $\pm$ 0.30 (0.09) & 0.611 $\pm$ 0.172 (0.054) \\
 & MWM$^\dagger$ & Fisher & -- & 1.05 $\pm$ 0.29 (0.09) & 0.607 $\pm$ 0.170 (0.054) \\
 & NRSur & Fisher & -- & 1.00 $\pm$ 0.26 (0.08) & 0.578 $\pm$ 0.151 (0.048) \\
 & MWM & Fisher$^\star$ & 13.1 $\pm$ 1.3 (0.4)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{ET+CE}} \\
 & MWM & Fisher & -- & 1.11 $\pm$ 0.28 (0.09) & 0.638 $\pm$ 0.163 (0.051) \\
 & MWM$^\dagger$ & Fisher & -- & 1.10 $\pm$ 0.28 (0.09) & 0.634 $\pm$ 0.161 (0.051) \\
 & NRSur & Fisher & -- & 1.06 $\pm$ 0.24 (0.08) & 0.611 $\pm$ 0.141 (0.045) \\
 & MWM & Fisher$^\star$ & 11.7 $\pm$ 1.0 (0.3)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{LISA (light seeds)}} \\
 & MWM & Fisher & -- & 341.9 $\pm$ 118.5 (37.5) & 108.1 $\pm$ 37.5 (11.8) \\
 & MWM$^\dagger$ & Fisher & -- & 304.2 $\pm$ 87.5 (27.7) & 96.2 $\pm$ 27.7 (8.7) \\
 & NRSur & Fisher & -- & 274.2 $\pm$ 80.5 (25.5) & 86.7 $\pm$ 25.5 (8.0) \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{LISA (heavy seeds)}} \\
 & MWM & Fisher & -- & 510.9 $\pm$ 389.3 (123.1) & 255.4 $\pm$ 194.6 (61.6) \\
 & MWM$^\dagger$ & Fisher & -- & 355.3 $\pm$ 204.1 (64.6) & 177.6 $\pm$ 102.1 (32.3) \\
 & NRSur & Fisher & -- & 453.0 $\pm$ 305.4 (96.6) & 226.5 $\pm$ 152.7 (48.3) \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\bottomrule
\end{tabular}
\begin{minipage}{\linewidth}
\smallskip\small
\textit{Notes:} $^\dagger$ MWM waveform with NRSur7dq2 prior bounds ($q\geq0.5$, $|\chi|\leq0.8$). $^\star$ Direct Fisher result for nearby-only population; no $\sqrt{N}$ scaling applied.
\end{minipage}
\end{table*}