\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 & -- & 46.1 $\pm$ 5.3 (1.7) & 28.2 $\pm$ 3.3 (1.0) \\
 & MWM$^\dagger$ & Fisher & -- & 45.8 $\pm$ 5.4 (1.7) & 28.0 $\pm$ 3.3 (1.0) \\
 & NRSur & Fisher & -- & 45.6 $\pm$ 5.9 (1.9) & 27.9 $\pm$ 3.6 (1.1) \\
 & 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 & -- & 2.42 $\pm$ 0.85 (0.27) & 1.40 $\pm$ 0.49 (0.16) \\
 & MWM$^\dagger$ & Fisher & -- & 2.39 $\pm$ 0.83 (0.26) & 1.38 $\pm$ 0.48 (0.15) \\
 & NRSur & Fisher & -- & 2.23 $\pm$ 0.79 (0.25) & 1.29 $\pm$ 0.46 (0.14) \\
 & 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 & -- & 1.79 $\pm$ 0.75 (0.24) & 1.04 $\pm$ 0.43 (0.14) \\
 & MWM$^\dagger$ & Fisher & -- & 1.77 $\pm$ 0.72 (0.23) & 1.02 $\pm$ 0.42 (0.13) \\
 & NRSur & Fisher & -- & 1.44 $\pm$ 0.52 (0.16) & 0.832 $\pm$ 0.299 (0.095) \\
 & 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 & -- & 2.07 $\pm$ 0.81 (0.26) & 1.20 $\pm$ 0.47 (0.15) \\
 & MWM$^\dagger$ & Fisher & -- & 2.04 $\pm$ 0.77 (0.24) & 1.18 $\pm$ 0.45 (0.14) \\
 & 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 & -- & 604.1 $\pm$ 431.5 (136.4) & 191.0 $\pm$ 136.4 (43.1) \\
 & MWM$^\dagger$ & Fisher & -- & 508.6 $\pm$ 352.4 (111.4) & 160.8 $\pm$ 111.4 (35.2) \\
 & NRSur & Fisher & -- & 620.3 $\pm$ 380.6 (120.4) & 196.2 $\pm$ 120.4 (38.1) \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{LISA (heavy seeds)}} \\
 & MWM & Fisher & -- & 131.2 $\pm$ 142.4 (45.0) & 65.6 $\pm$ 71.2 (22.5) \\
 & MWM$^\dagger$ & Fisher & -- & 126.6 $\pm$ 147.4 (46.6) & 63.3 $\pm$ 73.7 (23.3) \\
 & NRSur & Fisher & -- & 143.8 $\pm$ 139.4 (44.1) & 71.9 $\pm$ 69.7 (22.0) \\
 &  & 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*}