\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 & -- & 55.6 $\pm$ 6.0 (1.9) & 34.0 $\pm$ 3.6 (1.2) \\
 & 4 & 5 & -- & -- & 100 & MWM & -- & 54.4 $\pm$ 5.7 (1.8) & 33.3 $\pm$ 3.5 (1.1) \\
 & 16 & 5 & -- & -- & 100 & MWM & -- & 56.6 $\pm$ 6.6 (2.1) & 34.6 $\pm$ 4.1 (1.3) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 55.6 $\pm$ 6.0 (1.9) & 34.1 $\pm$ 3.7 (1.2) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 61.2 $\pm$ 6.4 (2.0) & 37.5 $\pm$ 3.9 (1.2) \\
 & 8 & 60 & -- & -- & 100 & MWM & -- & 66.4 $\pm$ 5.7 (1.8) & 40.7 $\pm$ 3.5 (1.1) \\
 & 8 & 5 & -- & -- & 80 & MWM & -- & 56.0 $\pm$ 6.3 (2.0) & 34.3 $\pm$ 3.9 (1.2) \\
 & 8 & 5 & -- & -- & 100 & MWM$^\dagger$ & -- & 52.5 $\pm$ 6.2 (2.0) & 32.1 $\pm$ 3.8 (1.2) \\
 & 8 & 5 & -- & -- & 100 & MWM & 277.3 $\pm$ 33.8 (10.7)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 2.27 $\pm$ 0.65 (0.21) & 1.31 $\pm$ 0.38 (0.12) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 2.18 $\pm$ 0.61 (0.19) & 1.26 $\pm$ 0.35 (0.11) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 2.31 $\pm$ 0.65 (0.21) & 1.34 $\pm$ 0.38 (0.12) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 2.29 $\pm$ 0.66 (0.21) & 1.32 $\pm$ 0.38 (0.12) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 2.57 $\pm$ 0.74 (0.23) & 1.48 $\pm$ 0.43 (0.13) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 2.63 $\pm$ 0.80 (0.25) & 1.52 $\pm$ 0.46 (0.15) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 2.29 $\pm$ 0.64 (0.20) & 1.32 $\pm$ 0.37 (0.12) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 2.08 $\pm$ 0.54 (0.17) & 1.20 $\pm$ 0.31 (0.10) \\
 & 8 & 2 & -- & -- & 100 & MWM & 23.3 $\pm$ 1.5 (0.5)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 2.33 $\pm$ 0.56 (0.18) & 1.34 $\pm$ 0.33 (0.10) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 2.22 $\pm$ 0.49 (0.16) & 1.28 $\pm$ 0.28 (0.09) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 2.40 $\pm$ 0.64 (0.20) & 1.38 $\pm$ 0.37 (0.12) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 2.33 $\pm$ 0.56 (0.18) & 1.34 $\pm$ 0.33 (0.10) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 3.01 $\pm$ 0.95 (0.30) & 1.74 $\pm$ 0.55 (0.17) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 2.67 $\pm$ 0.62 (0.20) & 1.54 $\pm$ 0.36 (0.11) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 2.33 $\pm$ 0.56 (0.18) & 1.34 $\pm$ 0.33 (0.10) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 2.27 $\pm$ 0.61 (0.19) & 1.31 $\pm$ 0.35 (0.11) \\
 & 8 & 2 & -- & -- & 100 & MWM & 11.3 $\pm$ 1.9 (0.6)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET+CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 2.47 $\pm$ 0.65 (0.20) & 1.43 $\pm$ 0.37 (0.12) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 2.28 $\pm$ 0.70 (0.22) & 1.32 $\pm$ 0.40 (0.13) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 2.53 $\pm$ 0.67 (0.21) & 1.46 $\pm$ 0.39 (0.12) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 2.48 $\pm$ 0.65 (0.20) & 1.43 $\pm$ 0.37 (0.12) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 2.84 $\pm$ 1.05 (0.33) & 1.64 $\pm$ 0.61 (0.19) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 2.69 $\pm$ 0.90 (0.28) & 1.55 $\pm$ 0.52 (0.16) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 2.48 $\pm$ 0.65 (0.21) & 1.43 $\pm$ 0.37 (0.12) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 2.39 $\pm$ 0.67 (0.21) & 1.38 $\pm$ 0.39 (0.12) \\
 & 8 & 2 & -- & -- & 100 & MWM & 10.1 $\pm$ 1.4 (0.4)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{LISA (light seeds)}} \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM & -- & 469.8 $\pm$ 338.8 (107.1) & 148.6 $\pm$ 107.1 (33.9) \\
 & -- & -- & 4096 & 10000 & $10^{6}$ & MWM & -- & 472.1 $\pm$ 339.3 (107.3) & 149.3 $\pm$ 107.3 (33.9) \\
 & -- & -- & 8192 & 10000 & $10^{6}$ & MWM & -- & 464.3 $\pm$ 338.7 (107.1) & 146.8 $\pm$ 107.1 (33.9) \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM$^\dagger$ & -- & 386.1 $\pm$ 229.3 (72.5) & 122.1 $\pm$ 72.5 (22.9) \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & NRSur & -- & 383.0 $\pm$ 251.0 (79.4) & 121.1 $\pm$ 79.4 (25.1) \\
\midrule
\multicolumn{10}{l}{\textit{LISA (heavy seeds)}} \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM & -- & 408.1 $\pm$ 315.7 (99.8) & 204.0 $\pm$ 157.9 (49.9) \\
 & -- & -- & 4096 & $10^{6}$ & $10^{8}$ & MWM & -- & 102.1 $\pm$ 120.9 (38.2) & 51.1 $\pm$ 60.5 (19.1) \\
 & -- & -- & 8192 & $10^{6}$ & $10^{8}$ & MWM & -- & 194.4 $\pm$ 185.8 (58.8) & 97.2 $\pm$ 92.9 (29.4) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM$^\dagger$ & -- & 478.3 $\pm$ 341.0 (107.8) & 239.1 $\pm$ 170.5 (53.9) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & NRSur & -- & 457.3 $\pm$ 281.1 (88.9) & 228.7 $\pm$ 140.6 (44.5) \\
\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*}