\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}{lrrrrrrccc}
\toprule
\multirow{2}{*}{Detector} & \multirow{2}{*}{$T_\mathrm{obs}$} & \multirow{2}{*}{$f_\mathrm{min}$} & \multirow{2}{*}{$N_\mathrm{samp}$} & \multirow{2}{*}{$M_\mathrm{min}$} & \multirow{2}{*}{$M_\mathrm{max}$} & \multirow{2}{*}{Approx.} & \multicolumn{3}{c}{$\sigma_{H_0}$ [km\,s$^{-1}$\,Mpc$^{-1}$]} \\
\cmidrule(lr){8-10}
 & [yr] & [Hz] &  & [$M_\odot$] & [$M_\odot$] &  & $N=100$ & $N_\mathrm{lo}$ & $N_\mathrm{hi}$ \\
\midrule
\multicolumn{10}{l}{\textit{CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & 15.6 $\pm$ 5.1 (1.0) & 0.156 $\pm$ 0.051 (0.010) & 0.090 $\pm$ 0.029 (0.006) \\
 & 4 & 2 & -- & -- & 100 & MWM & 15.5 $\pm$ 5.1 (1.0) & 0.155 $\pm$ 0.051 (0.010) & 0.090 $\pm$ 0.029 (0.006) \\
 & 16 & 2 & -- & -- & 100 & MWM & 15.6 $\pm$ 5.1 (1.0) & 0.156 $\pm$ 0.051 (0.010) & 0.090 $\pm$ 0.030 (0.006) \\
 & 8 & 5 & -- & -- & 100 & MWM & 15.6 $\pm$ 5.1 (1.0) & 0.156 $\pm$ 0.051 (0.010) & 0.090 $\pm$ 0.029 (0.006) \\
 & 8 & 20 & -- & -- & 100 & MWM & 21.2 $\pm$ 9.6 (1.9) & 0.212 $\pm$ 0.096 (0.019) & 0.122 $\pm$ 0.056 (0.011) \\
 & 8 & 40 & -- & -- & 100 & MWM & 24.7 $\pm$ 8.2 (1.6) & 0.247 $\pm$ 0.082 (0.016) & 0.143 $\pm$ 0.048 (0.010) \\
 & 8 & 2 & -- & -- & 80 & MWM & 17.1 $\pm$ 5.4 (1.1) & 0.171 $\pm$ 0.054 (0.011) & 0.099 $\pm$ 0.031 (0.006) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & 13.0 $\pm$ 3.9 (0.8) & 0.130 $\pm$ 0.039 (0.008) & 0.075 $\pm$ 0.022 (0.004) \\
\midrule
\multicolumn{10}{l}{\textit{ET+CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & 15.2 $\pm$ 5.3 (1.1) & 0.152 $\pm$ 0.053 (0.011) & 0.088 $\pm$ 0.030 (0.006) \\
 & 4 & 2 & -- & -- & 100 & MWM & 15.2 $\pm$ 5.2 (1.0) & 0.152 $\pm$ 0.052 (0.010) & 0.088 $\pm$ 0.030 (0.006) \\
 & 16 & 2 & -- & -- & 100 & MWM & 15.2 $\pm$ 5.3 (1.1) & 0.152 $\pm$ 0.053 (0.011) & 0.088 $\pm$ 0.030 (0.006) \\
 & 8 & 5 & -- & -- & 100 & MWM & 15.2 $\pm$ 5.3 (1.1) & 0.152 $\pm$ 0.053 (0.011) & 0.088 $\pm$ 0.030 (0.006) \\
 & 8 & 20 & -- & -- & 100 & MWM & 17.1 $\pm$ 5.5 (1.1) & 0.171 $\pm$ 0.055 (0.011) & 0.099 $\pm$ 0.032 (0.006) \\
 & 8 & 40 & -- & -- & 100 & MWM & 25.2 $\pm$ 8.0 (1.6) & 0.252 $\pm$ 0.080 (0.016) & 0.145 $\pm$ 0.046 (0.009) \\
 & 8 & 2 & -- & -- & 80 & MWM & 16.8 $\pm$ 5.6 (1.1) & 0.168 $\pm$ 0.056 (0.011) & 0.097 $\pm$ 0.032 (0.006) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & 13.3 $\pm$ 4.6 (0.9) & 0.133 $\pm$ 0.046 (0.009) & 0.077 $\pm$ 0.027 (0.005) \\
\midrule
\multicolumn{10}{l}{\textit{ET}} \\
 & 8 & 2 & -- & -- & 100 & MWM & 31.3 $\pm$ 8.7 (1.7) & 0.313 $\pm$ 0.087 (0.017) & 0.181 $\pm$ 0.050 (0.010) \\
 & 4 & 2 & -- & -- & 100 & MWM & 31.1 $\pm$ 8.6 (1.7) & 0.311 $\pm$ 0.086 (0.017) & 0.180 $\pm$ 0.050 (0.010) \\
 & 16 & 2 & -- & -- & 100 & MWM & 31.9 $\pm$ 8.9 (1.8) & 0.319 $\pm$ 0.089 (0.018) & 0.184 $\pm$ 0.051 (0.010) \\
 & 8 & 5 & -- & -- & 100 & MWM & 31.7 $\pm$ 8.8 (1.8) & 0.317 $\pm$ 0.088 (0.018) & 0.183 $\pm$ 0.051 (0.010) \\
 & 8 & 20 & -- & -- & 100 & MWM & 48.7 $\pm$ 12.7 (2.5) & 0.487 $\pm$ 0.127 (0.025) & 0.281 $\pm$ 0.073 (0.015) \\
 & 8 & 40 & -- & -- & 100 & MWM & 48.6 $\pm$ 9.8 (2.0) & 0.486 $\pm$ 0.098 (0.020) & 0.281 $\pm$ 0.057 (0.011) \\
 & 8 & 2 & -- & -- & 80 & MWM & 34.6 $\pm$ 9.3 (1.9) & 0.346 $\pm$ 0.093 (0.019) & 0.200 $\pm$ 0.054 (0.011) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & 28.2 $\pm$ 9.4 (1.9) & 0.282 $\pm$ 0.094 (0.019) & 0.163 $\pm$ 0.054 (0.011) \\
\midrule
\multicolumn{10}{l}{\textit{LISA (heavy seeds)}} \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM & 3.74 $\pm$ 2.22 (0.44) & 16.7 $\pm$ 9.9 (2.0) & 8.37 $\pm$ 4.97 (0.99) \\
 & -- & -- & 4096 & $10^{6}$ & $10^{8}$ & MWM & 1.24 $\pm$ 0.58 (0.12) & 5.53 $\pm$ 2.61 (0.52) & 2.76 $\pm$ 1.31 (0.26) \\
 & -- & -- & 8192 & $10^{6}$ & $10^{8}$ & MWM & 2.69 $\pm$ 0.96 (0.19) & 12.0 $\pm$ 4.3 (0.9) & 6.02 $\pm$ 2.16 (0.43) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM$^\dagger$ & 3.03 $\pm$ 1.77 (0.35) & 13.6 $\pm$ 7.9 (1.6) & 6.78 $\pm$ 3.97 (0.79) \\
\midrule
\multicolumn{10}{l}{\textit{LISA (light seeds)}} \\
 & -- & -- & 4096 & 10000 & $10^{6}$ & MWM & 6.88 $\pm$ 3.16 (0.63) & 30.8 $\pm$ 14.2 (2.8) & 9.73 $\pm$ 4.48 (0.90) \\
 & -- & -- & 8192 & 10000 & $10^{6}$ & MWM & 6.91 $\pm$ 3.15 (0.63) & 30.9 $\pm$ 14.1 (2.8) & 9.77 $\pm$ 4.46 (0.89) \\
\midrule
\multicolumn{10}{l}{\textit{aLIGO/Virgo}} \\
 & 4 & 5 & -- & -- & 100 & MWM & 61.1 $\pm$ 7.2 (1.4) & 11.2 $\pm$ 1.3 (0.3) & 6.83 $\pm$ 0.80 (0.16) \\
 & 8 & 40 & -- & -- & 100 & MWM & 66.8 $\pm$ 8.1 (1.6) & 12.2 $\pm$ 1.5 (0.3) & 7.47 $\pm$ 0.91 (0.18) \\
 & 8 & 60 & -- & -- & 100 & MWM & 71.5 $\pm$ 8.6 (1.7) & 13.0 $\pm$ 1.6 (0.3) & 7.99 $\pm$ 0.97 (0.19) \\
\bottomrule
\multicolumn{10}{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*}