\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 & -- & 46.1 $\pm$ 5.3 (1.7) & 28.2 $\pm$ 3.3 (1.0) \\
 & 4 & 5 & -- & -- & 100 & MWM & -- & 46.1 $\pm$ 5.3 (1.7) & 28.2 $\pm$ 3.3 (1.0) \\
 & 16 & 5 & -- & -- & 100 & MWM & -- & 46.3 $\pm$ 5.6 (1.8) & 28.3 $\pm$ 3.4 (1.1) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 46.2 $\pm$ 5.4 (1.7) & 28.3 $\pm$ 3.3 (1.0) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 51.2 $\pm$ 4.6 (1.5) & 31.4 $\pm$ 2.8 (0.9) \\
 & 8 & 60 & -- & -- & 100 & MWM & -- & 61.7 $\pm$ 4.9 (1.5) & 37.8 $\pm$ 3.0 (0.9) \\
 & 8 & 5 & -- & -- & 80 & MWM & -- & 46.1 $\pm$ 5.3 (1.7) & 28.3 $\pm$ 3.3 (1.0) \\
 & 8 & 5 & -- & -- & 100 & MWM$^\dagger$ & -- & 45.8 $\pm$ 5.4 (1.7) & 28.0 $\pm$ 3.3 (1.0) \\
 & 8 & 5 & -- & -- & 100 & NRSur & -- & 45.6 $\pm$ 5.9 (1.9) & 27.9 $\pm$ 3.6 (1.1) \\
 & 8 & 5 & -- & -- & 100 & MWM & 160.3 $\pm$ 12.8 (4.0)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 2.42 $\pm$ 0.85 (0.27) & 1.40 $\pm$ 0.49 (0.16) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 2.17 $\pm$ 0.69 (0.22) & 1.26 $\pm$ 0.40 (0.13) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 2.51 $\pm$ 0.93 (0.29) & 1.45 $\pm$ 0.54 (0.17) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 2.45 $\pm$ 0.86 (0.27) & 1.41 $\pm$ 0.50 (0.16) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 2.94 $\pm$ 0.84 (0.27) & 1.70 $\pm$ 0.49 (0.15) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 2.75 $\pm$ 0.94 (0.30) & 1.59 $\pm$ 0.54 (0.17) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 2.37 $\pm$ 0.83 (0.26) & 1.37 $\pm$ 0.48 (0.15) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 2.39 $\pm$ 0.83 (0.26) & 1.38 $\pm$ 0.48 (0.15) \\
 & 8 & 2 & -- & -- & 100 & NRSur & -- & 2.23 $\pm$ 0.79 (0.25) & 1.29 $\pm$ 0.46 (0.14) \\
 & 8 & 2 & -- & -- & 100 & MWM & 10.6 $\pm$ 0.7 (0.2)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 1.79 $\pm$ 0.75 (0.24) & 1.04 $\pm$ 0.43 (0.14) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 1.79 $\pm$ 0.75 (0.24) & 1.03 $\pm$ 0.43 (0.14) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 1.79 $\pm$ 0.75 (0.24) & 1.04 $\pm$ 0.43 (0.14) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 1.79 $\pm$ 0.75 (0.24) & 1.04 $\pm$ 0.43 (0.14) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 2.18 $\pm$ 1.06 (0.34) & 1.26 $\pm$ 0.61 (0.19) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 2.47 $\pm$ 0.83 (0.26) & 1.42 $\pm$ 0.48 (0.15) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 1.80 $\pm$ 0.75 (0.24) & 1.04 $\pm$ 0.43 (0.14) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 1.77 $\pm$ 0.72 (0.23) & 1.02 $\pm$ 0.42 (0.13) \\
 & 8 & 2 & -- & -- & 100 & NRSur & -- & 1.44 $\pm$ 0.52 (0.16) & 0.832 $\pm$ 0.299 (0.095) \\
 & 8 & 2 & -- & -- & 100 & MWM & 5.31 $\pm$ 0.58 (0.18)$^\star$ & -- & -- \\
\midrule
\multicolumn{10}{l}{\textit{ET+CE}} \\
 & 8 & 2 & -- & -- & 100 & MWM & -- & 2.07 $\pm$ 0.81 (0.26) & 1.20 $\pm$ 0.47 (0.15) \\
 & 4 & 2 & -- & -- & 100 & MWM & -- & 2.06 $\pm$ 0.81 (0.26) & 1.19 $\pm$ 0.47 (0.15) \\
 & 16 & 2 & -- & -- & 100 & MWM & -- & 2.07 $\pm$ 0.81 (0.26) & 1.20 $\pm$ 0.47 (0.15) \\
 & 8 & 5 & -- & -- & 100 & MWM & -- & 2.08 $\pm$ 0.82 (0.26) & 1.20 $\pm$ 0.47 (0.15) \\
 & 8 & 20 & -- & -- & 100 & MWM & -- & 2.56 $\pm$ 1.24 (0.39) & 1.48 $\pm$ 0.71 (0.23) \\
 & 8 & 40 & -- & -- & 100 & MWM & -- & 2.67 $\pm$ 0.98 (0.31) & 1.54 $\pm$ 0.56 (0.18) \\
 & 8 & 2 & -- & -- & 80 & MWM & -- & 2.08 $\pm$ 0.81 (0.26) & 1.20 $\pm$ 0.47 (0.15) \\
 & 8 & 2 & -- & -- & 100 & MWM$^\dagger$ & -- & 2.04 $\pm$ 0.77 (0.24) & 1.18 $\pm$ 0.45 (0.14) \\
 & 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 & -- & 604.1 $\pm$ 431.5 (136.4) & 191.0 $\pm$ 136.4 (43.1) \\
 & -- & -- & 4096 & 10000 & $10^{6}$ & MWM & -- & 502.3 $\pm$ 385.6 (121.9) & 158.8 $\pm$ 121.9 (38.6) \\
 & -- & -- & 8192 & 10000 & $10^{6}$ & MWM & -- & 604.2 $\pm$ 431.3 (136.4) & 191.1 $\pm$ 136.4 (43.1) \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & MWM$^\dagger$ & -- & 508.6 $\pm$ 352.4 (111.4) & 160.8 $\pm$ 111.4 (35.2) \\
 & -- & -- & 16384 & 10000 & $10^{6}$ & NRSur & -- & 620.3 $\pm$ 380.6 (120.4) & 196.2 $\pm$ 120.4 (38.1) \\
\midrule
\multicolumn{10}{l}{\textit{LISA (heavy seeds)}} \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM & -- & 131.2 $\pm$ 142.4 (45.0) & 65.6 $\pm$ 71.2 (22.5) \\
 & -- & -- & 4096 & $10^{6}$ & $10^{8}$ & MWM & -- & 125.9 $\pm$ 235.2 (74.4) & 62.9 $\pm$ 117.6 (37.2) \\
 & -- & -- & 8192 & $10^{6}$ & $10^{8}$ & MWM & -- & 94.0 $\pm$ 114.7 (36.3) & 47.0 $\pm$ 57.4 (18.1) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & MWM$^\dagger$ & -- & 126.6 $\pm$ 147.4 (46.6) & 63.3 $\pm$ 73.7 (23.3) \\
 & -- & -- & 16384 & $10^{6}$ & $10^{8}$ & NRSur & -- & 143.8 $\pm$ 139.4 (44.1) & 71.9 $\pm$ 69.7 (22.0) \\
\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*}