\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) \\
 & NRSur & Fisher & -- & 1.62 $\pm$ 0.27 (0.09) & 0.934 $\pm$ 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) & 0.613 $\pm$ 0.172 (0.054) \\
 & MWM$^\dagger$ & Fisher & -- & 1.05 $\pm$ 0.29 (0.09) & 0.609 $\pm$ 0.170 (0.054) \\
 & NRSur & Fisher & -- & 1.00 $\pm$ 0.26 (0.08) & 0.580 $\pm$ 0.151 (0.048) \\
 & 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 & -- & 342.1 $\pm$ 119.8 (37.9) & 108.2 $\pm$ 37.9 (12.0) \\
 & MWM$^\dagger$ & Fisher & -- & 304.4 $\pm$ 88.7 (28.1) & 96.2 $\pm$ 28.1 (8.9) \\
 & NRSur & Fisher & -- & 275.7 $\pm$ 81.2 (25.7) & 87.2 $\pm$ 25.7 (8.1) \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{LISA (heavy seeds)}} \\
 & MWM & Fisher & -- & 503.1 $\pm$ 396.8 (125.5) & 251.5 $\pm$ 198.4 (62.7) \\
 & MWM$^\dagger$ & Fisher & -- & 346.9 $\pm$ 208.3 (65.9) & 173.5 $\pm$ 104.1 (32.9) \\
 & NRSur & Fisher & -- & 444.3 $\pm$ 299.2 (94.6) & 222.2 $\pm$ 149.6 (47.3) \\
 &  & 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*}