\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 & -- & 96.1 $\pm$ 33.4 (10.6) & 58.8 $\pm$ 20.4 (6.5) \\
 & 4 & 5 & -- & -- & 100 & MWM & -- & 96.5 $\pm$ 34.0 (10.7) & 59.1 $\pm$ 20.8 (6.6) \\
 & 16 & 5 & -- & -- & 100 & MWM & -- & 97.2 $\pm$ 32.7 (10.3) & 59.5 $\pm$ 20.0 (6.3) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 96.2 $\pm$ 33.4 (10.6) & 58.9 $\pm$ 20.4 (6.5) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 109.0 $\pm$ 28.0 (8.9) & 66.7 $\pm$ 17.1 (5.4) \\
 & 8 & 60 & -- & -- & 100 & MWM & -- & 136.5 $\pm$ 32.9 (10.4) & 83.6 $\pm$ 20.1 (6.4) \\
 & 8 & 5 & -- & -- & 80 & MWM & -- & 96.2 $\pm$ 33.4 (10.6) & 58.9 $\pm$ 20.4 (6.5) \\
 & 8 & 5 & -- & -- & 100 & MWM$^\dagger$ & -- & 95.2 $\pm$ 33.2 (10.5) & 58.3 $\pm$ 20.3 (6.4) \\
 & 8 & 5 & -- & -- & 100 & NRSur & -- & 91.8 $\pm$ 21.6 (6.8) & 56.2 $\pm$ 13.3 (4.2) \\
 & 8 & 5 & -- & -- & 100 & MWM & 398.8 $\pm$ 32.4 (10.2)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 1.70 $\pm$ 0.33 (0.10) & 0.984 $\pm$ 0.191 (0.061) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 1.68 $\pm$ 0.36 (0.11) & 0.971 $\pm$ 0.205 (0.065) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 1.76 $\pm$ 0.31 (0.10) & 1.01 $\pm$ 0.18 (0.06) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 1.73 $\pm$ 0.33 (0.11) & 0.998 $\pm$ 0.193 (0.061) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 2.86 $\pm$ 0.54 (0.17) & 1.65 $\pm$ 0.31 (0.10) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 3.32 $\pm$ 0.63 (0.20) & 1.92 $\pm$ 0.36 (0.12) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 1.71 $\pm$ 0.33 (0.10) & 0.987 $\pm$ 0.190 (0.060) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 1.70 $\pm$ 0.32 (0.10) & 0.979 $\pm$ 0.187 (0.059) \\
 & 8 & 2 & -- & -- & 100 & NRSur & -- & 1.61 $\pm$ 0.27 (0.09) & 0.931 $\pm$ 0.158 (0.050) \\
 & 8 & 2 & -- & -- & 100 & MWM & 26.1 $\pm$ 1.6 (0.5)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 1.06 $\pm$ 0.30 (0.09) & 0.611 $\pm$ 0.172 (0.054) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 1.04 $\pm$ 0.26 (0.08) & 0.598 $\pm$ 0.152 (0.048) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 1.06 $\pm$ 0.30 (0.09) & 0.612 $\pm$ 0.171 (0.054) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 1.06 $\pm$ 0.30 (0.09) & 0.611 $\pm$ 0.172 (0.054) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 1.33 $\pm$ 0.34 (0.11) & 0.770 $\pm$ 0.196 (0.062) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 2.17 $\pm$ 0.65 (0.20) & 1.25 $\pm$ 0.37 (0.12) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 1.06 $\pm$ 0.30 (0.09) & 0.612 $\pm$ 0.171 (0.054) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 1.05 $\pm$ 0.29 (0.09) & 0.607 $\pm$ 0.170 (0.054) \\
 & 8 & 2 & -- & -- & 100 & NRSur & -- & 1.00 $\pm$ 0.26 (0.08) & 0.578 $\pm$ 0.151 (0.048) \\
 & 8 & 2 & -- & -- & 100 & MWM & 13.1 $\pm$ 1.3 (0.4)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET+CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 1.11 $\pm$ 0.28 (0.09) & 0.638 $\pm$ 0.163 (0.051) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 1.11 $\pm$ 0.28 (0.09) & 0.638 $\pm$ 0.163 (0.051) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 1.11 $\pm$ 0.27 (0.09) & 0.643 $\pm$ 0.157 (0.050) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 1.11 $\pm$ 0.28 (0.09) & 0.640 $\pm$ 0.164 (0.052) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 1.52 $\pm$ 0.38 (0.12) & 0.876 $\pm$ 0.220 (0.069) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 2.29 $\pm$ 0.56 (0.18) & 1.32 $\pm$ 0.32 (0.10) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 1.11 $\pm$ 0.28 (0.09) & 0.639 $\pm$ 0.163 (0.051) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 1.10 $\pm$ 0.28 (0.09) & 0.634 $\pm$ 0.161 (0.051) \\
 & 8 & 2 & -- & -- & 100 & NRSur & -- & 1.06 $\pm$ 0.24 (0.08) & 0.611 $\pm$ 0.141 (0.045) \\
 & 8 & 2 & -- & -- & 100 & MWM & 11.7 $\pm$ 1.0 (0.3)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{LISA (light seeds)}} \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM & -- & 341.9 $\pm$ 118.5 (37.5) & 108.1 $\pm$ 37.5 (11.8) \\
 & -- & -- & 4096 & 10000 & $10^{6}$ & MWM & -- & 335.9 $\pm$ 111.6 (35.3) & 106.2 $\pm$ 35.3 (11.2) \\
 & -- & -- & 8192 & 10000 & $10^{6}$ & MWM & -- & 338.4 $\pm$ 115.3 (36.5) & 107.0 $\pm$ 36.5 (11.5) \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM$^\dagger$ & -- & 304.2 $\pm$ 87.5 (27.7) & 96.2 $\pm$ 27.7 (8.7) \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & NRSur & -- & 274.2 $\pm$ 80.5 (25.5) & 86.7 $\pm$ 25.5 (8.0) \\
\midrule
\multicolumn{10}{l}{\textit{LISA (heavy seeds)}} \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM & -- & 510.9 $\pm$ 389.3 (123.1) & 255.4 $\pm$ 194.6 (61.6) \\
 & -- & -- & 4096 & $10^{6}$ & $10^{8}$ & MWM & -- & 517.3 $\pm$ 306.8 (97.0) & 258.7 $\pm$ 153.4 (48.5) \\
 & -- & -- & 8192 & $10^{6}$ & $10^{8}$ & MWM & -- & 518.4 $\pm$ 370.9 (117.3) & 259.2 $\pm$ 185.5 (58.7) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM$^\dagger$ & -- & 355.3 $\pm$ 204.1 (64.6) & 177.6 $\pm$ 102.1 (32.3) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & NRSur & -- & 453.0 $\pm$ 305.4 (96.6) & 226.5 $\pm$ 152.7 (48.3) \\
\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*}