\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 & -- & 55.6 $\pm$ 6.0 (1.9) & 34.0 $\pm$ 3.6 (1.2) \\
 & MWM$^\dagger$ & Fisher & -- & 52.5 $\pm$ 6.2 (2.0) & 32.1 $\pm$ 3.8 (1.2) \\
 & MWM & Fisher$^\star$ & 277.3 $\pm$ 33.8 (10.7)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{ET}} \\
 & MWM & Fisher & -- & 2.27 $\pm$ 0.65 (0.21) & 1.31 $\pm$ 0.38 (0.12) \\
 & MWM$^\dagger$ & Fisher & -- & 2.08 $\pm$ 0.54 (0.17) & 1.20 $\pm$ 0.31 (0.10) \\
 & MWM & Fisher$^\star$ & 23.3 $\pm$ 1.5 (0.5)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{CE}} \\
 & MWM & Fisher & -- & 2.33 $\pm$ 0.56 (0.18) & 1.34 $\pm$ 0.33 (0.10) \\
 & MWM$^\dagger$ & Fisher & -- & 2.27 $\pm$ 0.61 (0.19) & 1.31 $\pm$ 0.35 (0.11) \\
 & MWM & Fisher$^\star$ & 11.3 $\pm$ 1.9 (0.6)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{ET+CE}} \\
 & MWM & Fisher & -- & 2.47 $\pm$ 0.65 (0.20) & 1.43 $\pm$ 0.37 (0.12) \\
 & MWM$^\dagger$ & Fisher & -- & 2.39 $\pm$ 0.67 (0.21) & 1.38 $\pm$ 0.39 (0.12) \\
 & MWM & Fisher$^\star$ & 10.1 $\pm$ 1.4 (0.4)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{LISA (light seeds)}} \\
 & MWM & Fisher & -- & 469.8 $\pm$ 338.8 (107.1) & 148.6 $\pm$ 107.1 (33.9) \\
 & MWM$^\dagger$ & Fisher & -- & 386.1 $\pm$ 229.3 (72.5) & 122.1 $\pm$ 72.5 (22.9) \\
 & NRSur & Fisher & -- & 383.0 $\pm$ 251.0 (79.4) & 121.1 $\pm$ 79.4 (25.1) \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{LISA (heavy seeds)}} \\
 & MWM & Fisher & -- & 408.1 $\pm$ 315.7 (99.8) & 204.0 $\pm$ 157.9 (49.9) \\
 & MWM$^\dagger$ & Fisher & -- & 478.3 $\pm$ 341.0 (107.8) & 239.1 $\pm$ 170.5 (53.9) \\
 & NRSur & Fisher & -- & 457.3 $\pm$ 281.1 (88.9) & 228.7 $\pm$ 140.6 (44.5) \\
 &  & 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*}