\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 & -- & 100.4 $\pm$ 41.2 (13.0) & 61.5 $\pm$ 25.2 (8.0) \\
 & 4 & 5 & -- & -- & 100 & MWM & -- & 100.7 $\pm$ 41.5 (13.1) & 61.7 $\pm$ 25.4 (8.0) \\
 & 16 & 5 & -- & -- & 100 & MWM & -- & 101.8 $\pm$ 40.5 (12.8) & 62.3 $\pm$ 24.8 (7.8) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 100.5 $\pm$ 41.2 (13.0) & 61.6 $\pm$ 25.3 (8.0) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 112.8 $\pm$ 31.0 (9.8) & 69.1 $\pm$ 19.0 (6.0) \\
 & 8 & 60 & -- & -- & 100 & MWM & -- & 142.2 $\pm$ 35.4 (11.2) & 87.1 $\pm$ 21.7 (6.9) \\
 & 8 & 5 & -- & -- & 80 & MWM & -- & 100.5 $\pm$ 41.2 (13.0) & 61.6 $\pm$ 25.3 (8.0) \\
 & 8 & 5 & -- & -- & 100 & MWM$^\dagger$ & -- & 99.3 $\pm$ 40.9 (12.9) & 60.8 $\pm$ 25.0 (7.9) \\
 & 8 & 5 & -- & -- & 100 & MWM & 400.3 $\pm$ 32.3 (10.2)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 1.71 $\pm$ 0.33 (0.11) & 0.987 $\pm$ 0.192 (0.061) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 1.69 $\pm$ 0.36 (0.11) & 0.974 $\pm$ 0.206 (0.065) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 1.76 $\pm$ 0.32 (0.10) & 1.02 $\pm$ 0.18 (0.06) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 1.73 $\pm$ 0.34 (0.11) & 1.00 $\pm$ 0.19 (0.06) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 2.87 $\pm$ 0.54 (0.17) & 1.66 $\pm$ 0.31 (0.10) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 3.34 $\pm$ 0.62 (0.20) & 1.93 $\pm$ 0.36 (0.11) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 1.72 $\pm$ 0.33 (0.10) & 0.990 $\pm$ 0.191 (0.060) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 1.70 $\pm$ 0.32 (0.10) & 0.982 $\pm$ 0.187 (0.059) \\
 & 8 & 2 & -- & -- & 100 & NRSur & -- & 1.62 $\pm$ 0.27 (0.09) & 0.934 $\pm$ 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) & 0.613 $\pm$ 0.172 (0.054) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 1.04 $\pm$ 0.26 (0.08) & 0.600 $\pm$ 0.152 (0.048) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 1.06 $\pm$ 0.30 (0.09) & 0.614 $\pm$ 0.172 (0.054) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 1.06 $\pm$ 0.30 (0.09) & 0.613 $\pm$ 0.172 (0.054) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 1.34 $\pm$ 0.34 (0.11) & 0.773 $\pm$ 0.196 (0.062) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 2.18 $\pm$ 0.65 (0.21) & 1.26 $\pm$ 0.38 (0.12) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 1.06 $\pm$ 0.30 (0.09) & 0.614 $\pm$ 0.172 (0.054) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 1.05 $\pm$ 0.29 (0.09) & 0.609 $\pm$ 0.170 (0.054) \\
 & 8 & 2 & -- & -- & 100 & NRSur & -- & 1.00 $\pm$ 0.26 (0.08) & 0.580 $\pm$ 0.151 (0.048) \\
 & 8 & 2 & -- & -- & 100 & MWM & 13.2 $\pm$ 1.3 (0.4)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET+CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 1.11 $\pm$ 0.28 (0.09) & 0.643 $\pm$ 0.161 (0.051) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 1.11 $\pm$ 0.28 (0.09) & 0.640 $\pm$ 0.163 (0.052) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 1.12 $\pm$ 0.27 (0.09) & 0.646 $\pm$ 0.157 (0.050) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 1.12 $\pm$ 0.28 (0.09) & 0.645 $\pm$ 0.162 (0.051) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 1.52 $\pm$ 0.38 (0.12) & 0.879 $\pm$ 0.220 (0.070) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 2.30 $\pm$ 0.56 (0.18) & 1.33 $\pm$ 0.32 (0.10) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 1.11 $\pm$ 0.28 (0.09) & 0.643 $\pm$ 0.161 (0.051) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 1.11 $\pm$ 0.28 (0.09) & 0.638 $\pm$ 0.159 (0.050) \\
 & 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 & -- & 342.1 $\pm$ 119.8 (37.9) & 108.2 $\pm$ 37.9 (12.0) \\
 & -- & -- & 4096 & 10000 & $10^{6}$ & MWM & -- & 336.8 $\pm$ 112.1 (35.5) & 106.5 $\pm$ 35.5 (11.2) \\
 & -- & -- & 8192 & 10000 & $10^{6}$ & MWM & -- & 339.7 $\pm$ 115.6 (36.6) & 107.4 $\pm$ 36.6 (11.6) \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM$^\dagger$ & -- & 304.4 $\pm$ 88.7 (28.1) & 96.2 $\pm$ 28.1 (8.9) \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & NRSur & -- & 275.7 $\pm$ 81.2 (25.7) & 87.2 $\pm$ 25.7 (8.1) \\
\midrule
\multicolumn{10}{l}{\textit{LISA (heavy seeds)}} \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM & -- & 503.1 $\pm$ 396.8 (125.5) & 251.5 $\pm$ 198.4 (62.7) \\
 & -- & -- & 4096 & $10^{6}$ & $10^{8}$ & MWM & -- & 518.9 $\pm$ 307.3 (97.2) & 259.4 $\pm$ 153.7 (48.6) \\
 & -- & -- & 8192 & $10^{6}$ & $10^{8}$ & MWM & -- & 523.9 $\pm$ 376.9 (119.2) & 262.0 $\pm$ 188.4 (59.6) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM$^\dagger$ & -- & 346.9 $\pm$ 208.3 (65.9) & 173.5 $\pm$ 104.1 (32.9) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & NRSur & -- & 444.3 $\pm$ 299.2 (94.6) & 222.2 $\pm$ 149.6 (47.3) \\
\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*}