\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{LISA (light seeds)}} \\
 & MWM$^\dagger$ & Fisher & -- & 810.2 & 181.2 \\
 &  & Bayesian & \hspace{2em} & \hspace{2em} & \hspace{2em} \\
\midrule
\multicolumn{6}{l}{\textit{LISA (heavy seeds)}} \\
 & MWM$^\dagger$ & Fisher & -- & -- & -- \\
 & MWM$^\dagger$ & Fisher & -- & -- & -- \\
 &  & 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*}