\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 & -- & 59.2 $\pm$ 7.7 (5.4) & 36.3 $\pm$ 4.7 (3.3) \\
 & 4 & 5 & -- & -- & 100 & MWM & -- & 57.9 $\pm$ 9.0 (6.4) & 35.4 $\pm$ 5.5 (3.9) \\
 & 16 & 5 & -- & -- & 100 & MWM & -- & 59.7 $\pm$ 7.3 (5.2) & 36.5 $\pm$ 4.5 (3.2) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 59.3 $\pm$ 7.7 (5.4) & 36.3 $\pm$ 4.7 (3.3) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 66.6 $\pm$ 6.1 (4.3) & 40.8 $\pm$ 3.8 (2.7) \\
 & 8 & 60 & -- & -- & 100 & MWM & -- & 69.2 $\pm$ 2.1 (1.5) & 42.4 $\pm$ 1.3 (0.9) \\
 & 8 & 5 & -- & -- & 80 & MWM & -- & 59.5 $\pm$ 9.0 (6.3) & 36.4 $\pm$ 5.5 (3.9) \\
 & 8 & 5 & -- & -- & 100 & MWM$^\dagger$ & -- & 57.1 $\pm$ 10.7 (7.6) & 35.0 $\pm$ 6.6 (4.6) \\
 & 8 & 5 & -- & -- & 100 & MWM & 293.8 $\pm$ 48.3 (34.1)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 2.20 $\pm$ 0.12 (0.09) & 1.27 $\pm$ 0.07 (0.05) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 2.10 $\pm$ 0.19 (0.13) & 1.21 $\pm$ 0.11 (0.08) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 2.29 $\pm$ 0.26 (0.18) & 1.32 $\pm$ 0.15 (0.10) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 2.21 $\pm$ 0.11 (0.08) & 1.27 $\pm$ 0.06 (0.04) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 2.89 $\pm$ 1.24 (0.88) & 1.67 $\pm$ 0.72 (0.51) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 3.11 $\pm$ 1.30 (0.92) & 1.80 $\pm$ 0.75 (0.53) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 2.21 $\pm$ 0.13 (0.09) & 1.27 $\pm$ 0.07 (0.05) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 2.05 $\pm$ 0.16 (0.12) & 1.18 $\pm$ 0.09 (0.07) \\
 & 8 & 2 & -- & -- & 100 & MWM & 23.6 $\pm$ 2.4 (1.7)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 1.88 $\pm$ 0.59 (0.41) & 1.09 $\pm$ 0.34 (0.24) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 1.84 $\pm$ 0.52 (0.37) & 1.06 $\pm$ 0.30 (0.21) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 1.92 $\pm$ 0.62 (0.44) & 1.11 $\pm$ 0.36 (0.25) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 1.88 $\pm$ 0.59 (0.41) & 1.09 $\pm$ 0.34 (0.24) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 2.77 $\pm$ 1.40 (0.99) & 1.60 $\pm$ 0.81 (0.57) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 2.73 $\pm$ 0.63 (0.45) & 1.58 $\pm$ 0.37 (0.26) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 1.88 $\pm$ 0.58 (0.41) & 1.09 $\pm$ 0.34 (0.24) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 1.82 $\pm$ 0.68 (0.48) & 1.05 $\pm$ 0.39 (0.28) \\
 & 8 & 2 & -- & -- & 100 & MWM & 13.0 $\pm$ 2.4 (1.7)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET+CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 2.05 $\pm$ 0.66 (0.47) & 1.18 $\pm$ 0.38 (0.27) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 2.03 $\pm$ 0.63 (0.45) & 1.17 $\pm$ 0.36 (0.26) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 2.08 $\pm$ 0.70 (0.50) & 1.20 $\pm$ 0.41 (0.29) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 2.05 $\pm$ 0.67 (0.47) & 1.19 $\pm$ 0.38 (0.27) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 3.31 $\pm$ 2.02 (1.43) & 1.91 $\pm$ 1.17 (0.82) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 2.01 $\pm$ 0.65 (0.46) & 1.16 $\pm$ 0.38 (0.27) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 2.05 $\pm$ 0.66 (0.47) & 1.18 $\pm$ 0.38 (0.27) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 1.99 $\pm$ 0.77 (0.54) & 1.15 $\pm$ 0.44 (0.31) \\
 & 8 & 2 & -- & -- & 100 & MWM & 11.4 $\pm$ 2.0 (1.4)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{LISA (light seeds)}} \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM & -- & 474.6 $\pm$ 299.8 (212.0) & 150.1 $\pm$ 94.8 (67.0) \\
 & -- & -- & 4096 & 10000 & $10^{6}$ & MWM & -- & 450.8 $\pm$ 299.9 (212.0) & 142.6 $\pm$ 94.8 (67.0) \\
 & -- & -- & 8192 & 10000 & $10^{6}$ & MWM & -- & 450.9 $\pm$ 299.9 (212.1) & 142.6 $\pm$ 94.8 (67.1) \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM$^\dagger$ & -- & 333.3 $\pm$ 203.1 (143.6) & 105.4 $\pm$ 64.2 (45.4) \\
\midrule
\multicolumn{10}{l}{\textit{LISA (heavy seeds)}} \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM & -- & 366.7 $\pm$ 199.6 (141.1) & 183.3 $\pm$ 99.8 (70.6) \\
 & -- & -- & 4096 & $10^{6}$ & $10^{8}$ & MWM & -- & 168.0 $\pm$ 109.3 (77.3) & 84.0 $\pm$ 54.7 (38.7) \\
 & -- & -- & 8192 & $10^{6}$ & $10^{8}$ & MWM & -- & 268.2 $\pm$ 60.3 (42.6) & 134.1 $\pm$ 30.1 (21.3) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM$^\dagger$ & -- & 547.2 $\pm$ 81.4 (57.6) & 273.6 $\pm$ 40.7 (28.8) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & NRSur & -- & 705.6 $\pm$ 47.6 (33.7) & 352.8 $\pm$ 23.8 (16.8) \\
\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*}