\begin{table*}[ht]
\centering
\caption{Fisher $1\sigma$ uncertainties on $H_0$ from GW memory. The column $N=100$ gives the direct Fisher constraint from a dedicated run restricted to $d_{L,\mathrm{near}}=100$\,events (marked $^\star$); it is only shown for those rows and is left blank for full-volume runs where such scaling would be misleading. $N_\mathrm{lo}$ and $N_\mathrm{hi}$ are the expected total detections over the full detectable volume at the low and high merger rate bounds (shown only for full-volume 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
Detector & $T_\mathrm{obs}$ & $f_\mathrm{min}$ & $M_\mathrm{max}$ & Approx. & \multicolumn{3}{c}{$\sigma_{H_0}$ [km\,s$^{-1}$\,Mpc$^{-1}$]} \\
\cmidrule(r){1-5}\cmidrule(lr){6-8}
 & [yr] & [Hz] & [$M_\odot$] &  & $N=100$ & $N_\mathrm{lo}$ & $N_\mathrm{hi}$ \\
\midrule
\multicolumn{8}{l}{\textit{aLIGO/Virgo}} \\
 & 8 & 5 & 100 & MWM & -- & 10.3 $\pm$ 2.2 (0.7) & 6.30 $\pm$ 1.34 (0.42) \\
 & 4 & 5 & 100 & MWM & -- & 9.95 $\pm$ 2.14 (0.68) & 6.10 $\pm$ 1.31 (0.41) \\
 & 8 & 20 & 100 & MWM & -- & 10.3 $\pm$ 2.2 (0.7) & 6.31 $\pm$ 1.34 (0.42) \\
 & 8 & 40 & 100 & MWM & -- & 11.2 $\pm$ 2.9 (0.9) & 6.88 $\pm$ 1.75 (0.55) \\
 & 8 & 60 & 100 & MWM & -- & 9.87 $\pm$ 1.27 (0.40) & 6.04 $\pm$ 0.78 (0.25) \\
 & 8 & 5 & 80 & MWM & -- & 10.3 $\pm$ 2.2 (0.7) & 6.32 $\pm$ 1.35 (0.43) \\
 & 8 & 5 & 100 & MWM$^\dagger$ & -- & 9.90 $\pm$ 1.84 (0.58) & 6.06 $\pm$ 1.12 (0.36) \\
\midrule
\multicolumn{8}{l}{\textit{ET}} \\
 & 8 & 2 & 100 & MWM & -- & 1.04 $\pm$ 0.41 (0.13) & 0.602 $\pm$ 0.234 (0.074) \\
 & 4 & 2 & 100 & MWM & -- & 0.923 $\pm$ 0.417 (0.132) & 0.533 $\pm$ 0.241 (0.076) \\
 & 16 & 2 & 100 & MWM & -- & 1.12 $\pm$ 0.39 (0.12) & 0.646 $\pm$ 0.228 (0.072) \\
 & 8 & 5 & 100 & MWM & -- & 1.05 $\pm$ 0.41 (0.13) & 0.608 $\pm$ 0.237 (0.075) \\
 & 8 & 20 & 100 & MWM & -- & 1.00 $\pm$ 0.31 (0.10) & 0.578 $\pm$ 0.179 (0.056) \\
 & 8 & 40 & 100 & MWM & -- & 0.925 $\pm$ 0.201 (0.064) & 0.534 $\pm$ 0.116 (0.037) \\
 & 8 & 2 & 80 & MWM & -- & 1.03 $\pm$ 0.38 (0.12) & 0.594 $\pm$ 0.221 (0.070) \\
 & 8 & 2 & 100 & MWM$^\dagger$ & -- & 1.01 $\pm$ 0.29 (0.09) & 0.582 $\pm$ 0.170 (0.054) \\
 & 8 & 2 & 100 & MWM & 4.63 $\pm$ 0.96 (0.30)$^\star$ & -- & -- \\
\midrule
\multicolumn{8}{l}{\textit{CE}} \\
 & 8 & 2 & 100 & MWM & -- & 1.09 $\pm$ 0.46 (0.15) & 0.629 $\pm$ 0.266 (0.084) \\
 & 4 & 2 & 100 & MWM & -- & 1.02 $\pm$ 0.40 (0.13) & 0.586 $\pm$ 0.234 (0.074) \\
\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*}