\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 & 61.5 $\pm$ 5.3 (1.9) & 11.2 $\pm$ 1.0 (0.3) & 6.88 $\pm$ 0.60 (0.21) \\
 & 4 & 5 & -- & -- & 100 & MWM & 61.7 $\pm$ 5.4 (1.9) & 11.3 $\pm$ 1.0 (0.4) & 6.89 $\pm$ 0.61 (0.21) \\
 & 8 & 20 & -- & -- & 100 & MWM & 61.6 $\pm$ 5.3 (1.9) & 11.2 $\pm$ 1.0 (0.3) & 6.89 $\pm$ 0.60 (0.21) \\
 & 8 & 40 & -- & -- & 100 & MWM & 64.6 $\pm$ 8.9 (3.1) & 11.8 $\pm$ 1.6 (0.6) & 7.22 $\pm$ 0.99 (0.35) \\
 & 8 & 60 & -- & -- & 100 & MWM & 72.4 $\pm$ 8.6 (3.0) & 13.2 $\pm$ 1.6 (0.6) & 8.09 $\pm$ 0.96 (0.34) \\
 & 8 & 5 & -- & -- & 80 & MWM & 61.6 $\pm$ 5.2 (1.8) & 11.2 $\pm$ 0.9 (0.3) & 6.88 $\pm$ 0.58 (0.20) \\
 & 8 & 5 & -- & -- & 100 & MWM$^\dagger$ & 54.7 $\pm$ 5.0 (1.8) & 9.99 $\pm$ 0.91 (0.32) & 6.12 $\pm$ 0.56 (0.20) \\
 & 8 & 5 & -- & -- & 100 & MWM & 61.5 $\pm$ 5.3 (1.9) & 11.2 $\pm$ 1.0 (0.3) & 6.88 $\pm$ 0.60 (0.21) \\
\midrule
\multicolumn{10}{l}{\textit{ET}} \\
 & 8 & 2 & -- & -- & 100 & MWM & 27.1 $\pm$ 4.4 (1.6) & 0.271 $\pm$ 0.044 (0.016) & 0.156 $\pm$ 0.025 (0.009) \\
 & 4 & 2 & -- & -- & 100 & MWM & 27.0 $\pm$ 4.4 (1.6) & 0.270 $\pm$ 0.044 (0.016) & 0.156 $\pm$ 0.025 (0.009) \\
 & 16 & 2 & -- & -- & 100 & MWM & 28.1 $\pm$ 4.8 (1.7) & 0.281 $\pm$ 0.048 (0.017) & 0.162 $\pm$ 0.028 (0.010) \\
 & 8 & 5 & -- & -- & 100 & MWM & 27.4 $\pm$ 4.5 (1.6) & 0.274 $\pm$ 0.045 (0.016) & 0.158 $\pm$ 0.026 (0.009) \\
 & 8 & 20 & -- & -- & 100 & MWM & 46.3 $\pm$ 4.7 (1.7) & 0.463 $\pm$ 0.047 (0.017) & 0.267 $\pm$ 0.027 (0.010) \\
 & 8 & 40 & -- & -- & 100 & MWM & 49.1 $\pm$ 9.8 (3.5) & 0.491 $\pm$ 0.098 (0.035) & 0.284 $\pm$ 0.057 (0.020) \\
 & 8 & 2 & -- & -- & 80 & MWM & 30.2 $\pm$ 4.9 (1.7) & 0.302 $\pm$ 0.049 (0.017) & 0.175 $\pm$ 0.028 (0.010) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & 23.5 $\pm$ 4.8 (1.7) & 0.235 $\pm$ 0.048 (0.017) & 0.136 $\pm$ 0.028 (0.010) \\
 & 8 & 2 & -- & -- & 100 & MWM & 27.1 $\pm$ 4.4 (1.6) & 0.271 $\pm$ 0.044 (0.016) & 0.156 $\pm$ 0.025 (0.009) \\
\midrule
\multicolumn{10}{l}{\textit{CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & 13.6 $\pm$ 4.2 (1.5) & 0.136 $\pm$ 0.042 (0.015) & 0.078 $\pm$ 0.024 (0.009) \\
 & 4 & 2 & -- & -- & 100 & MWM & 13.6 $\pm$ 4.2 (1.5) & 0.136 $\pm$ 0.042 (0.015) & 0.078 $\pm$ 0.024 (0.009) \\
 & 16 & 2 & -- & -- & 100 & MWM & 13.6 $\pm$ 4.2 (1.5) & 0.136 $\pm$ 0.042 (0.015) & 0.078 $\pm$ 0.024 (0.009) \\
 & 8 & 5 & -- & -- & 100 & MWM & 13.6 $\pm$ 4.2 (1.5) & 0.136 $\pm$ 0.042 (0.015) & 0.078 $\pm$ 0.024 (0.009) \\
 & 8 & 20 & -- & -- & 100 & MWM & 20.9 $\pm$ 9.9 (3.5) & 0.209 $\pm$ 0.099 (0.035) & 0.121 $\pm$ 0.057 (0.020) \\
 & 8 & 40 & -- & -- & 100 & MWM & 26.8 $\pm$ 10.7 (3.8) & 0.268 $\pm$ 0.107 (0.038) & 0.155 $\pm$ 0.062 (0.022) \\
 & 8 & 2 & -- & -- & 80 & MWM & 15.0 $\pm$ 4.5 (1.6) & 0.150 $\pm$ 0.045 (0.016) & 0.087 $\pm$ 0.026 (0.009) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & 11.9 $\pm$ 2.8 (1.0) & 0.119 $\pm$ 0.028 (0.010) & 0.069 $\pm$ 0.016 (0.006) \\
 & 8 & 2 & -- & -- & 100 & MWM & 13.6 $\pm$ 4.2 (1.5) & 0.136 $\pm$ 0.042 (0.015) & 0.078 $\pm$ 0.024 (0.009) \\
\midrule
\multicolumn{10}{l}{\textit{ET+CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & 14.0 $\pm$ 5.0 (1.8) & 0.140 $\pm$ 0.050 (0.018) & 0.081 $\pm$ 0.029 (0.010) \\
 & 4 & 2 & -- & -- & 100 & MWM & 14.0 $\pm$ 4.9 (1.7) & 0.140 $\pm$ 0.049 (0.017) & 0.081 $\pm$ 0.029 (0.010) \\
 & 16 & 2 & -- & -- & 100 & MWM & 14.1 $\pm$ 5.1 (1.8) & 0.141 $\pm$ 0.051 (0.018) & 0.081 $\pm$ 0.029 (0.010) \\
 & 8 & 5 & -- & -- & 100 & MWM & 14.1 $\pm$ 5.0 (1.8) & 0.141 $\pm$ 0.050 (0.018) & 0.081 $\pm$ 0.029 (0.010) \\
 & 8 & 20 & -- & -- & 100 & MWM & 16.4 $\pm$ 3.0 (1.1) & 0.164 $\pm$ 0.030 (0.011) & 0.095 $\pm$ 0.017 (0.006) \\
 & 8 & 40 & -- & -- & 100 & MWM & 26.3 $\pm$ 2.6 (0.9) & 0.263 $\pm$ 0.026 (0.009) & 0.152 $\pm$ 0.015 (0.005) \\
 & 8 & 2 & -- & -- & 80 & MWM & 15.6 $\pm$ 5.4 (1.9) & 0.156 $\pm$ 0.054 (0.019) & 0.090 $\pm$ 0.031 (0.011) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & 11.5 $\pm$ 3.1 (1.1) & 0.115 $\pm$ 0.031 (0.011) & 0.066 $\pm$ 0.018 (0.006) \\
 & 8 & 2 & -- & -- & 100 & MWM & 14.0 $\pm$ 5.0 (1.8) & 0.140 $\pm$ 0.050 (0.018) & 0.081 $\pm$ 0.029 (0.010) \\
\midrule
\multicolumn{10}{l}{\textit{LISA (light seeds)}} \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM & 7.22 $\pm$ 2.57 (0.91) & 32.3 $\pm$ 11.5 (4.1) & 10.2 $\pm$ 3.6 (1.3) \\
 & -- & -- & 4096 & 10000 & $10^{6}$ & MWM & 7.02 $\pm$ 2.95 (1.04) & 31.4 $\pm$ 13.2 (4.7) & 9.93 $\pm$ 4.17 (1.48) \\
 & -- & -- & 8192 & 10000 & $10^{6}$ & MWM & 7.07 $\pm$ 2.95 (1.04) & 31.6 $\pm$ 13.2 (4.7) & 10.00 $\pm$ 4.17 (1.47) \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM$^\dagger$ & 6.67 $\pm$ 2.58 (0.91) & 29.8 $\pm$ 11.6 (4.1) & 9.43 $\pm$ 3.65 (1.29) \\
\midrule
\multicolumn{10}{l}{\textit{LISA (heavy seeds)}} \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM & 5.31 $\pm$ 3.30 (1.17) & 23.8 $\pm$ 14.8 (5.2) & 11.9 $\pm$ 7.4 (2.6) \\
 & -- & -- & 4096 & $10^{6}$ & $10^{8}$ & MWM & 1.13 $\pm$ 0.67 (0.24) & 5.06 $\pm$ 2.98 (1.05) & 2.53 $\pm$ 1.49 (0.53) \\
 & -- & -- & 8192 & $10^{6}$ & $10^{8}$ & MWM & 3.09 $\pm$ 1.35 (0.48) & 13.8 $\pm$ 6.0 (2.1) & 6.92 $\pm$ 3.02 (1.07) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM$^\dagger$ & 4.32 $\pm$ 2.62 (0.93) & 19.3 $\pm$ 11.7 (4.1) & 9.67 $\pm$ 5.87 (2.07) \\
\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*}