\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 & -- & 100.4 $\pm$ 41.2 (13.0) & 61.5 $\pm$ 25.2 (8.0) \\
 & MWM$^\dagger$ & Fisher & -- & 99.3 $\pm$ 40.9 (12.9) & 60.8 $\pm$ 25.0 (7.9) \\
 & MWM & Fisher$^\star$ & 400.3 $\pm$ 32.3 (10.2)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{ET}} \\
 & MWM & Fisher & -- & 1.71 $\pm$ 0.33 (0.11) & 0.987 $\pm$ 0.192 (0.061) \\
 & MWM$^\dagger$ & Fisher & -- & 1.70 $\pm$ 0.32 (0.10) & 0.982 $\pm$ 0.187 (0.059) \\
 & 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) & 0.613 $\pm$ 0.172 (0.054) \\
 & MWM$^\dagger$ & Fisher & -- & 1.05 $\pm$ 0.29 (0.09) & 0.609 $\pm$ 0.170 (0.054) \\
 & MWM & Fisher$^\star$ & 13.2 $\pm$ 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) & 0.643 $\pm$ 0.161 (0.051) \\
 & MWM$^\dagger$ & Fisher & -- & 1.11 $\pm$ 0.28 (0.09) & 0.638 $\pm$ 0.159 (0.050) \\
 & 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 & -- & 360.8 $\pm$ 151.2 (47.8) & 80.7 $\pm$ 33.8 (10.7) \\
 & MWM$^\dagger$ & Fisher & -- & 302.1 $\pm$ 106.4 (33.6) & 67.6 $\pm$ 23.8 (7.5) \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{LISA (heavy seeds)}} \\
 & MWM & Fisher & -- & 480.5 $\pm$ 260.0 (82.2) & 151.9 $\pm$ 82.2 (26.0) \\
 & MWM$^\dagger$ & Fisher & -- & 461.5 $\pm$ 269.1 (85.1) & 145.9 $\pm$ 85.1 (26.9) \\
 &  & 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*}