\begin{table*}[ht]
\centering
\caption{Fisher $1\sigma$ uncertainties on $H_0$ from GW memory. The column $N=100$ gives the constraint from exactly 100 detections within $d_{L,\mathrm{near}}$ (the volume used for Bayesian sampling). For rows marked $^\star$ this is the direct Fisher result from a dedicated run restricted to $d_{L,\mathrm{near}}$; for other rows it is obtained by Fisher scaling $\sigma(N_{100}) = \sigma_{N_\mathrm{det}}\sqrt{N_\mathrm{det}/100}$ from the full-volume run. $N_\mathrm{lo}$ and $N_\mathrm{hi}$ are the expected total detections over the full detectable volume at the low and high merger rate bounds (suppressed for nearby-only runs). Each cell shows mean\,$\pm$\,population scatter\,($\sigma_\mathrm{pop}$) with Monte Carlo error in parentheses.}
\label{tab:sigma_H0_combined}
\begin{tabular}{lrrrrccc}
\toprule
\multirow{2}{*}{Detector} & \multirow{2}{*}{$T_\mathrm{obs}$} & \multirow{2}{*}{$f_\mathrm{min}$} & \multirow{2}{*}{$M_\mathrm{max}$} & \multirow{2}{*}{Approx.} & \multicolumn{3}{c}{$\sigma_{H_0}$ [km\,s$^{-1}$\,Mpc$^{-1}$]} \\
\cmidrule(lr){6-8}
 & [yr] & [Hz] & [$M_\odot$] &  & $N=100$ & $N_\mathrm{lo}$ & $N_\mathrm{hi}$ \\
\midrule
\multicolumn{8}{l}{\textit{ET}} \\
 & 4 & 2 & 100 & MWM & 25.3 $\pm$ 5.3 (2.6) & 0.253 $\pm$ 0.053 (0.026) & 0.146 $\pm$ 0.030 (0.015) \\
\bottomrule
\multicolumn{8}{l}{\footnotesize $^\dagger$ MWM waveform with NRSur7dq2 prior bounds ($q\geq0.5$, $|\chi|\leq0.8$). $^\star$ Direct Fisher result for nearby-only population ($d_L \leq d_{L,\mathrm{near}}$); no $\sqrt{N}$ scaling applied.}
\end{tabular}
\end{table*}