\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
Detector & $T_\mathrm{obs}$ & $f_\mathrm{min}$ & $N_\mathrm{samp}$ & $M_\mathrm{min}$ & $M_\mathrm{max}$ & Approx. & \multicolumn{3}{c}{$\sigma_{H_0}$ [km\,s$^{-1}$\,Mpc$^{-1}$]} \\
\cmidrule(r){1-7}\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 & -- & 48.3 $\pm$ 15.2 (4.8) & 29.6 $\pm$ 9.3 (2.9) \\
 & 4 & 5 & -- & -- & 100 & MWM & -- & 48.8 $\pm$ 16.1 (5.1) & 29.9 $\pm$ 9.8 (3.1) \\
 & 16 & 5 & -- & -- & 100 & MWM & -- & 48.8 $\pm$ 14.7 (4.6) & 29.9 $\pm$ 9.0 (2.8) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 48.4 $\pm$ 15.2 (4.8) & 29.6 $\pm$ 9.3 (2.9) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 50.5 $\pm$ 11.9 (3.8) & 30.9 $\pm$ 7.3 (2.3) \\
 & 8 & 60 & -- & -- & 100 & MWM & -- & 58.7 $\pm$ 15.2 (4.8) & 36.0 $\pm$ 9.3 (2.9) \\
 & 8 & 5 & -- & -- & 80 & MWM & -- & 48.3 $\pm$ 15.2 (4.8) & 29.6 $\pm$ 9.3 (2.9) \\
 & 8 & 5 & -- & -- & 100 & MWM$^\dagger$ & -- & 47.9 $\pm$ 15.2 (4.8) & 29.4 $\pm$ 9.3 (2.9) \\
 & 8 & 5 & -- & -- & 100 & MWM & 160.3 $\pm$ 12.8 (4.0)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 1.96 $\pm$ 0.44 (0.14) & 1.13 $\pm$ 0.26 (0.08) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 1.87 $\pm$ 0.44 (0.14) & 1.08 $\pm$ 0.25 (0.08) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 2.00 $\pm$ 0.46 (0.15) & 1.15 $\pm$ 0.26 (0.08) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 1.98 $\pm$ 0.45 (0.14) & 1.14 $\pm$ 0.26 (0.08) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 2.46 $\pm$ 0.85 (0.27) & 1.42 $\pm$ 0.49 (0.15) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 2.60 $\pm$ 0.77 (0.24) & 1.50 $\pm$ 0.44 (0.14) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 1.96 $\pm$ 0.44 (0.14) & 1.13 $\pm$ 0.26 (0.08) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 1.95 $\pm$ 0.44 (0.14) & 1.13 $\pm$ 0.25 (0.08) \\
 & 8 & 2 & -- & -- & 100 & MWM & 10.6 $\pm$ 0.7 (0.2)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 1.30 $\pm$ 0.41 (0.13) & 0.751 $\pm$ 0.239 (0.075) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 1.29 $\pm$ 0.40 (0.13) & 0.746 $\pm$ 0.232 (0.073) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 1.30 $\pm$ 0.41 (0.13) & 0.752 $\pm$ 0.239 (0.075) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 1.30 $\pm$ 0.41 (0.13) & 0.751 $\pm$ 0.239 (0.075) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 1.43 $\pm$ 0.46 (0.14) & 0.825 $\pm$ 0.263 (0.083) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 1.74 $\pm$ 0.41 (0.13) & 1.01 $\pm$ 0.23 (0.07) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 1.30 $\pm$ 0.42 (0.13) & 0.749 $\pm$ 0.241 (0.076) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 1.29 $\pm$ 0.41 (0.13) & 0.747 $\pm$ 0.236 (0.075) \\
 & 8 & 2 & -- & -- & 100 & MWM & 5.31 $\pm$ 0.58 (0.18)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET+CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 1.36 $\pm$ 0.37 (0.12) & 0.784 $\pm$ 0.216 (0.068) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 1.36 $\pm$ 0.37 (0.12) & 0.784 $\pm$ 0.216 (0.068) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 1.38 $\pm$ 0.36 (0.11) & 0.797 $\pm$ 0.210 (0.066) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 1.36 $\pm$ 0.38 (0.12) & 0.785 $\pm$ 0.217 (0.069) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 1.55 $\pm$ 0.45 (0.14) & 0.893 $\pm$ 0.259 (0.082) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 1.94 $\pm$ 0.58 (0.18) & 1.12 $\pm$ 0.33 (0.11) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 1.35 $\pm$ 0.38 (0.12) & 0.782 $\pm$ 0.218 (0.069) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 1.35 $\pm$ 0.37 (0.12) & 0.780 $\pm$ 0.213 (0.067) \\
 & 8 & 2 & -- & -- & 100 & MWM & 4.74 $\pm$ 0.45 (0.14)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{LISA (light seeds)}} \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM & -- & 175.5 $\pm$ 74.7 (23.6) & 55.5 $\pm$ 23.6 (7.5) \\
 & -- & -- & 4096 & 10000 & $10^{6}$ & MWM & -- & 174.5 $\pm$ 74.1 (23.4) & 55.2 $\pm$ 23.4 (7.4) \\
 & -- & -- & 8192 & 10000 & $10^{6}$ & MWM & -- & 175.1 $\pm$ 73.7 (23.3) & 55.4 $\pm$ 23.3 (7.4) \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM$^\dagger$ & -- & 164.0 $\pm$ 68.1 (21.5) & 51.9 $\pm$ 21.5 (6.8) \\
\midrule
\multicolumn{10}{l}{\textit{LISA (heavy seeds)}} \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM & -- & 107.7 $\pm$ 74.8 (23.7) & 53.8 $\pm$ 37.4 (11.8) \\
 & -- & -- & 4096 & $10^{6}$ & $10^{8}$ & MWM & -- & 15.4 $\pm$ 17.1 (5.4) & 7.71 $\pm$ 8.54 (2.70) \\
 & -- & -- & 8192 & $10^{6}$ & $10^{8}$ & MWM & -- & 38.3 $\pm$ 46.0 (14.5) & 19.2 $\pm$ 23.0 (7.3) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM$^\dagger$ & -- & 103.1 $\pm$ 65.1 (20.6) & 51.5 $\pm$ 32.5 (10.3) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & NRSur & -- & 82.2 $\pm$ 69.1 (21.8) & 41.1 $\pm$ 34.5 (10.9) \\
\bottomrule
\end{tabular}
\begin{minipage}{\linewidth}
\smallskip\small
\textit{Notes:} $^\dagger$ 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{minipage}
\end{table*}