\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}{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 & -- & 0.143 $\pm$ 0.040 (0.013) & 0.082 $\pm$ 0.023 (0.007) \\
 & 8 & 2 & -- & -- & 100 & MWM & 0.628 $\pm$ 0.049 (0.015)$^\star$ & -- & -- \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 0.142 $\pm$ 0.039 (0.012) & 0.082 $\pm$ 0.023 (0.007) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 0.144 $\pm$ 0.040 (0.013) & 0.083 $\pm$ 0.023 (0.007) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 0.143 $\pm$ 0.040 (0.013) & 0.082 $\pm$ 0.023 (0.007) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 0.208 $\pm$ 0.089 (0.028) & 0.120 $\pm$ 0.051 (0.016) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 0.264 $\pm$ 0.097 (0.031) & 0.152 $\pm$ 0.056 (0.018) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 0.158 $\pm$ 0.043 (0.014) & 0.091 $\pm$ 0.025 (0.008) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 0.122 $\pm$ 0.026 (0.008) & 0.071 $\pm$ 0.015 (0.005) \\
\midrule
\multicolumn{10}{l}{\textit{ET+CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 0.147 $\pm$ 0.047 (0.015) & 0.085 $\pm$ 0.027 (0.009) \\
 & 8 & 2 & -- & -- & 100 & MWM & 0.595 $\pm$ 0.046 (0.015)$^\star$ & -- & -- \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 0.147 $\pm$ 0.047 (0.015) & 0.085 $\pm$ 0.027 (0.009) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 0.147 $\pm$ 0.048 (0.015) & 0.085 $\pm$ 0.027 (0.009) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 0.147 $\pm$ 0.047 (0.015) & 0.085 $\pm$ 0.027 (0.009) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 0.172 $\pm$ 0.048 (0.015) & 0.099 $\pm$ 0.028 (0.009) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 0.263 $\pm$ 0.037 (0.012) & 0.152 $\pm$ 0.022 (0.007) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 0.163 $\pm$ 0.051 (0.016) & 0.094 $\pm$ 0.030 (0.009) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 0.120 $\pm$ 0.032 (0.010) & 0.069 $\pm$ 0.018 (0.006) \\
\midrule
\multicolumn{10}{l}{\textit{ET}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 0.286 $\pm$ 0.066 (0.021) & 0.165 $\pm$ 0.038 (0.012) \\
 & 8 & 2 & -- & -- & 100 & MWM & 1.86 $\pm$ 0.14 (0.04)$^\star$ & -- & -- \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 0.285 $\pm$ 0.067 (0.021) & 0.164 $\pm$ 0.039 (0.012) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 0.295 $\pm$ 0.068 (0.022) & 0.170 $\pm$ 0.039 (0.012) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 0.289 $\pm$ 0.067 (0.021) & 0.167 $\pm$ 0.039 (0.012) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 0.472 $\pm$ 0.053 (0.017) & 0.272 $\pm$ 0.031 (0.010) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 0.502 $\pm$ 0.098 (0.031) & 0.290 $\pm$ 0.057 (0.018) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 0.319 $\pm$ 0.074 (0.023) & 0.184 $\pm$ 0.043 (0.014) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 0.249 $\pm$ 0.064 (0.020) & 0.143 $\pm$ 0.037 (0.012) \\
\midrule
\multicolumn{10}{l}{\textit{LISA (heavy seeds)}} \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM & -- & 21.7 $\pm$ 13.8 (4.4) & 10.8 $\pm$ 6.9 (2.2) \\
 & -- & -- & 4096 & $10^{6}$ & $10^{8}$ & MWM & -- & 5.18 $\pm$ 2.76 (0.87) & 2.59 $\pm$ 1.38 (0.44) \\
 & -- & -- & 8192 & $10^{6}$ & $10^{8}$ & MWM & -- & 13.4 $\pm$ 5.5 (1.7) & 6.68 $\pm$ 2.73 (0.86) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM$^\dagger$ & -- & 17.8 $\pm$ 10.9 (3.5) & 8.89 $\pm$ 5.47 (1.73) \\
\midrule
\multicolumn{10}{l}{\textit{LISA (light seeds)}} \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM & -- & 31.5 $\pm$ 10.3 (3.3) & 9.95 $\pm$ 3.26 (1.03) \\
 & -- & -- & 4096 & 10000 & $10^{6}$ & MWM & -- & 30.7 $\pm$ 11.8 (3.7) & 9.70 $\pm$ 3.72 (1.18) \\
 & -- & -- & 8192 & 10000 & $10^{6}$ & MWM & -- & 30.8 $\pm$ 11.8 (3.7) & 9.74 $\pm$ 3.72 (1.18) \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM$^\dagger$ & -- & 30.3 $\pm$ 12.4 (3.9) & 9.57 $\pm$ 3.92 (1.24) \\
\midrule
\multicolumn{10}{l}{\textit{aLIGO/Virgo}} \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 11.2 $\pm$ 0.9 (0.3) & 6.83 $\pm$ 0.57 (0.18) \\
 & 8 & 5 & -- & -- & 100 & MWM & 22.1 $\pm$ 2.0 (0.6)$^\star$ & -- & -- \\
 & 4 & 5 & -- & -- & 100 & MWM & -- & 11.1 $\pm$ 0.9 (0.3) & 6.83 $\pm$ 0.58 (0.18) \\
 & 16 & 5 & -- & -- & 100 & MWM & -- & 11.2 $\pm$ 0.9 (0.3) & 6.84 $\pm$ 0.57 (0.18) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 11.2 $\pm$ 0.9 (0.3) & 6.84 $\pm$ 0.57 (0.18) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 11.8 $\pm$ 1.5 (0.5) & 7.22 $\pm$ 0.89 (0.28) \\
 & 8 & 60 & -- & -- & 100 & MWM & -- & 13.1 $\pm$ 1.4 (0.5) & 8.00 $\pm$ 0.88 (0.28) \\
 & 8 & 5 & -- & -- & 80 & MWM & -- & 11.2 $\pm$ 0.9 (0.3) & 6.84 $\pm$ 0.54 (0.17) \\
 & 8 & 5 & -- & -- & 100 & MWM$^\dagger$ & -- & 9.89 $\pm$ 0.87 (0.27) & 6.06 $\pm$ 0.53 (0.17) \\
\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*}