\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{aLIGO/Virgo}} \\
 & 8 & 5 & -- & -- & 100 & MWM & 60.0 $\pm$ 2.7 (1.4) & 11.0 $\pm$ 0.5 (0.2) & 6.71 $\pm$ 0.30 (0.15) \\
 & 4 & 5 & -- & -- & 100 & MWM & 59.9 $\pm$ 2.1 (1.0) & 10.9 $\pm$ 0.4 (0.2) & 6.70 $\pm$ 0.23 (0.12) \\
 & 8 & 20 & -- & -- & 100 & MWM & 60.0 $\pm$ 2.6 (1.3) & 11.0 $\pm$ 0.5 (0.2) & 6.71 $\pm$ 0.29 (0.14) \\
 & 8 & 40 & -- & -- & 100 & MWM & 65.8 $\pm$ 3.6 (1.8) & 12.0 $\pm$ 0.7 (0.3) & 7.36 $\pm$ 0.40 (0.20) \\
 & 8 & 60 & -- & -- & 100 & MWM & 74.5 $\pm$ 8.4 (4.2) & 13.6 $\pm$ 1.5 (0.8) & 8.33 $\pm$ 0.94 (0.47) \\
 & 8 & 5 & -- & -- & 80 & MWM & 60.5 $\pm$ 1.9 (0.9) & 11.0 $\pm$ 0.3 (0.2) & 6.76 $\pm$ 0.21 (0.11) \\
 & 8 & 5 & -- & -- & 100 & MWM$^\dagger$ & 52.7 $\pm$ 3.0 (1.5) & 9.62 $\pm$ 0.54 (0.27) & 5.89 $\pm$ 0.33 (0.17) \\
 & 8 & 5 & -- & -- & 100 & MWM & 21.3 $\pm$ 1.0 (0.5)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET}} \\
 & 8 & 2 & -- & -- & 100 & MWM & 25.4 $\pm$ 5.2 (2.6) & 0.254 $\pm$ 0.052 (0.026) & 0.146 $\pm$ 0.030 (0.015) \\
 & 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) \\
 & 16 & 2 & -- & -- & 100 & MWM & 25.4 $\pm$ 5.2 (2.6) & 0.254 $\pm$ 0.052 (0.026) & 0.147 $\pm$ 0.030 (0.015) \\
 & 8 & 5 & -- & -- & 100 & MWM & 25.7 $\pm$ 5.3 (2.6) & 0.257 $\pm$ 0.053 (0.026) & 0.148 $\pm$ 0.031 (0.015) \\
 & 8 & 20 & -- & -- & 100 & MWM & 47.7 $\pm$ 3.7 (1.8) & 0.477 $\pm$ 0.037 (0.018) & 0.275 $\pm$ 0.021 (0.011) \\
 & 8 & 40 & -- & -- & 100 & MWM & 53.0 $\pm$ 11.0 (5.5) & 0.530 $\pm$ 0.110 (0.055) & 0.306 $\pm$ 0.063 (0.032) \\
 & 8 & 2 & -- & -- & 80 & MWM & 28.4 $\pm$ 5.7 (2.8) & 0.284 $\pm$ 0.057 (0.028) & 0.164 $\pm$ 0.033 (0.016) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & 21.6 $\pm$ 5.5 (2.7) & 0.216 $\pm$ 0.055 (0.027) & 0.125 $\pm$ 0.032 (0.016) \\
 & 8 & 2 & -- & -- & 100 & MWM & 1.83 $\pm$ 0.12 (0.06)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & 11.9 $\pm$ 2.2 (1.1) & 0.119 $\pm$ 0.022 (0.011) & 0.069 $\pm$ 0.013 (0.006) \\
 & 4 & 2 & -- & -- & 100 & MWM & 11.9 $\pm$ 2.2 (1.1) & 0.119 $\pm$ 0.022 (0.011) & 0.069 $\pm$ 0.013 (0.006) \\
 & 16 & 2 & -- & -- & 100 & MWM & 11.9 $\pm$ 2.2 (1.1) & 0.119 $\pm$ 0.022 (0.011) & 0.069 $\pm$ 0.013 (0.006) \\
 & 8 & 5 & -- & -- & 100 & MWM & 11.9 $\pm$ 2.2 (1.1) & 0.119 $\pm$ 0.022 (0.011) & 0.069 $\pm$ 0.013 (0.006) \\
 & 8 & 20 & -- & -- & 100 & MWM & 17.0 $\pm$ 2.3 (1.2) & 0.170 $\pm$ 0.023 (0.012) & 0.098 $\pm$ 0.013 (0.007) \\
 & 8 & 40 & -- & -- & 100 & MWM & 30.6 $\pm$ 14.2 (7.1) & 0.306 $\pm$ 0.142 (0.071) & 0.177 $\pm$ 0.082 (0.041) \\
 & 8 & 2 & -- & -- & 80 & MWM & 13.2 $\pm$ 2.4 (1.2) & 0.132 $\pm$ 0.024 (0.012) & 0.076 $\pm$ 0.014 (0.007) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & 10.9 $\pm$ 2.9 (1.4) & 0.109 $\pm$ 0.029 (0.014) & 0.063 $\pm$ 0.017 (0.008) \\
 & 8 & 2 & -- & -- & 100 & MWM & 0.612 $\pm$ 0.041 (0.020)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET+CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & 12.3 $\pm$ 2.6 (1.3) & 0.123 $\pm$ 0.026 (0.013) & 0.071 $\pm$ 0.015 (0.007) \\
 & 4 & 2 & -- & -- & 100 & MWM & 12.3 $\pm$ 2.6 (1.3) & 0.123 $\pm$ 0.026 (0.013) & 0.071 $\pm$ 0.015 (0.007) \\
 & 16 & 2 & -- & -- & 100 & MWM & 12.3 $\pm$ 2.6 (1.3) & 0.123 $\pm$ 0.026 (0.013) & 0.071 $\pm$ 0.015 (0.007) \\
 & 8 & 5 & -- & -- & 100 & MWM & 12.3 $\pm$ 2.6 (1.3) & 0.123 $\pm$ 0.026 (0.013) & 0.071 $\pm$ 0.015 (0.007) \\
 & 8 & 20 & -- & -- & 100 & MWM & 17.4 $\pm$ 3.4 (1.7) & 0.174 $\pm$ 0.034 (0.017) & 0.101 $\pm$ 0.020 (0.010) \\
 & 8 & 40 & -- & -- & 100 & MWM & 27.3 $\pm$ 1.7 (0.8) & 0.273 $\pm$ 0.017 (0.008) & 0.158 $\pm$ 0.010 (0.005) \\
 & 8 & 2 & -- & -- & 80 & MWM & 13.6 $\pm$ 2.9 (1.4) & 0.136 $\pm$ 0.029 (0.014) & 0.079 $\pm$ 0.017 (0.008) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & 10.3 $\pm$ 2.0 (1.0) & 0.103 $\pm$ 0.020 (0.010) & 0.060 $\pm$ 0.011 (0.006) \\
 & 8 & 2 & -- & -- & 100 & MWM & 0.581 $\pm$ 0.039 (0.019)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{LISA (light seeds)}} \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM & 7.71 $\pm$ 3.22 (1.61) & 34.5 $\pm$ 14.4 (7.2) & 10.9 $\pm$ 4.5 (2.3) \\
 & -- & -- & 4096 & 10000 & $10^{6}$ & MWM & 7.38 $\pm$ 3.92 (1.96) & 33.0 $\pm$ 17.5 (8.8) & 10.4 $\pm$ 5.5 (2.8) \\
 & -- & -- & 8192 & 10000 & $10^{6}$ & MWM & 7.40 $\pm$ 3.93 (1.97) & 33.1 $\pm$ 17.6 (8.8) & 10.5 $\pm$ 5.6 (2.8) \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM$^\dagger$ & 5.91 $\pm$ 2.76 (1.38) & 26.4 $\pm$ 12.3 (6.2) & 8.35 $\pm$ 3.90 (1.95) \\
\midrule
\multicolumn{10}{l}{\textit{LISA (heavy seeds)}} \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM & 5.15 $\pm$ 3.97 (1.98) & 23.0 $\pm$ 17.8 (8.9) & 11.5 $\pm$ 8.9 (4.4) \\
 & -- & -- & 4096 & $10^{6}$ & $10^{8}$ & MWM & 0.693 $\pm$ 0.148 (0.074) & 3.10 $\pm$ 0.66 (0.33) & 1.55 $\pm$ 0.33 (0.17) \\
 & -- & -- & 8192 & $10^{6}$ & $10^{8}$ & MWM & 2.27 $\pm$ 0.96 (0.48) & 10.2 $\pm$ 4.3 (2.2) & 5.08 $\pm$ 2.15 (1.08) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM$^\dagger$ & 4.49 $\pm$ 3.25 (1.63) & 20.1 $\pm$ 14.5 (7.3) & 10.0 $\pm$ 7.3 (3.6) \\
\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*}