\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 & -- & 48.3 $\pm$ 15.2 (4.8) & 29.6 $\pm$ 9.3 (2.9) \\
 & MWM$^\dagger$ & Fisher & -- & 47.9 $\pm$ 15.2 (4.8) & 29.4 $\pm$ 9.3 (2.9) \\
 & MWM & Fisher$^\star$ & 160.3 $\pm$ 12.8 (4.0)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{ET}} \\
 & MWM & Fisher & -- & 1.96 $\pm$ 0.44 (0.14) & 1.13 $\pm$ 0.26 (0.08) \\
 & MWM$^\dagger$ & Fisher & -- & 1.95 $\pm$ 0.44 (0.14) & 1.13 $\pm$ 0.25 (0.08) \\
 & MWM & Fisher$^\star$ & 10.6 $\pm$ 0.7 (0.2)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{CE}} \\
 & MWM & Fisher & -- & 1.30 $\pm$ 0.41 (0.13) & 0.751 $\pm$ 0.239 (0.075) \\
 & MWM$^\dagger$ & Fisher & -- & 1.29 $\pm$ 0.41 (0.13) & 0.747 $\pm$ 0.236 (0.075) \\
 & MWM & Fisher$^\star$ & 5.31 $\pm$ 0.58 (0.18)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{ET+CE}} \\
 & MWM & Fisher & -- & 1.36 $\pm$ 0.37 (0.12) & 0.784 $\pm$ 0.216 (0.068) \\
 & MWM$^\dagger$ & Fisher & -- & 1.35 $\pm$ 0.37 (0.12) & 0.780 $\pm$ 0.213 (0.067) \\
 & MWM & Fisher$^\star$ & 4.74 $\pm$ 0.45 (0.14)$^\star$ & -- & -- \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{LISA (light seeds)}} \\
 & MWM & Fisher & -- & 175.5 $\pm$ 74.7 (23.6) & 55.5 $\pm$ 23.6 (7.5) \\
 & MWM$^\dagger$ & Fisher & -- & 164.0 $\pm$ 68.1 (21.5) & 51.9 $\pm$ 21.5 (6.8) \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{LISA (heavy seeds)}} \\
 & MWM & Fisher & -- & 107.7 $\pm$ 74.8 (23.7) & 53.8 $\pm$ 37.4 (11.8) \\
 & MWM$^\dagger$ & Fisher & -- & 103.1 $\pm$ 65.1 (20.6) & 51.5 $\pm$ 32.5 (10.3) \\
 & NRSur & Fisher & -- & 82.2 $\pm$ 69.1 (21.8) & 41.1 $\pm$ 34.5 (10.9) \\
 &  & 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*}