\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 & -- & 59.2 $\pm$ 7.7 (5.4) & 36.3 $\pm$ 4.7 (3.3) \\
 & MWM$^\dagger$ & Fisher & -- & 57.1 $\pm$ 10.7 (7.6) & 35.0 $\pm$ 6.6 (4.6) \\
 & MWM & Fisher$^\star$ & 293.8 $\pm$ 48.3 (34.1)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{ET}} \\
 & MWM & Fisher & -- & 2.20 $\pm$ 0.12 (0.09) & 1.27 $\pm$ 0.07 (0.05) \\
 & MWM$^\dagger$ & Fisher & -- & 2.05 $\pm$ 0.16 (0.12) & 1.18 $\pm$ 0.09 (0.07) \\
 & MWM & Fisher$^\star$ & 23.6 $\pm$ 2.4 (1.7)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{CE}} \\
 & MWM & Fisher & -- & 1.88 $\pm$ 0.59 (0.41) & 1.09 $\pm$ 0.34 (0.24) \\
 & MWM$^\dagger$ & Fisher & -- & 1.82 $\pm$ 0.68 (0.48) & 1.05 $\pm$ 0.39 (0.28) \\
 & NRSur & Fisher & -- & 2.02 $\pm$ 0.72 (0.51) & 1.17 $\pm$ 0.41 (0.29) \\
 & MWM & Fisher$^\star$ & 13.0 $\pm$ 2.4 (1.7)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{ET+CE}} \\
 & MWM & Fisher & -- & 2.05 $\pm$ 0.66 (0.47) & 1.18 $\pm$ 0.38 (0.27) \\
 & MWM$^\dagger$ & Fisher & -- & 1.99 $\pm$ 0.77 (0.54) & 1.15 $\pm$ 0.44 (0.31) \\
 & MWM & Fisher$^\star$ & 11.4 $\pm$ 2.0 (1.4)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{LISA (light seeds)}} \\
 & MWM & Fisher & -- & 474.6 $\pm$ 299.8 (212.0) & 150.1 $\pm$ 94.8 (67.0) \\
 & MWM$^\dagger$ & Fisher & -- & 333.3 $\pm$ 203.1 (143.6) & 105.4 $\pm$ 64.2 (45.4) \\
 & NRSur & Fisher & -- & 394.6 $\pm$ 255.2 (180.4) & 124.8 $\pm$ 80.7 (57.1) \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{LISA (heavy seeds)}} \\
 & MWM & Fisher & -- & 366.7 $\pm$ 199.6 (141.1) & 183.3 $\pm$ 99.8 (70.6) \\
 & MWM$^\dagger$ & Fisher & -- & 547.0 $\pm$ 81.8 (57.8) & 273.5 $\pm$ 40.9 (28.9) \\
 & NRSur & Fisher & -- & 705.6 $\pm$ 47.6 (33.7) & 352.8 $\pm$ 23.8 (16.8) \\
 &  & 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*}