% Table 4: Full OAT results — includes low-mass boundary rows for ground-based detectors
\begin{table*}[ht]
\centering
\caption{Fisher $1\sigma$ uncertainties on $H_0$ [$\kms$] from GW memory, scanning baseline
parameter variations one-at-a-time (OAT). The $N\!=\!100^\star$ column gives the direct
Fisher result for $d_L\!\leq\!700$\,Mpc; $N_{\rm lo}$/$N_{\rm hi}$ are full-volume
projections at the low/high merger-rate bounds. The mass range column shows
$[M_{\rm min}, M_{\rm max}]$\,[$M_\odot$]; a dash indicates the detector default is used
(no lower cut applied for the baseline; low-mass boundary rows show explicit lower limits).
Each cell: mean\,$\pm$\,scatter (MC error).}
\label{tab:sigma_H0_combined}
\setlength{\tabcolsep}{4pt}
{\small
\begin{tabular}{l l r r r c c c c}
\toprule
Det. & Approx. & $T_{\rm obs}$\,[yr] & $f_{\rm min}$\,[Hz] & $N_{\rm samp}$ & $M$\,range\,[$M_\odot$] &
  $N\!=\!100^\star$ & $N_{\rm lo}$ & $N_{\rm hi}$ \\
\midrule
%% -----------------------------------------------
%% aLIGO/Virgo
%% -----------------------------------------------
HLV & MWM & 8 & 5 & -- & $[{-},{100}]$ & $160.3\pm12.8(4.0)^\star$ & $48.3\pm15.2(4.8)$ & $29.6\pm9.3(2.9)$ \\
 & MWM & 4 & 5 & -- & $[{-},{100}]$ & -- & $48.8\pm16.1(5.1)$ & $29.9\pm9.8(3.1)$ \\
 & MWM & 16 & 5 & -- & $[{-},{100}]$ & -- & $48.8\pm14.7(4.6)$ & $29.9\pm9.0(2.8)$ \\
 & MWM & 8 & 20 & -- & $[{-},{100}]$ & -- & $48.4\pm15.2(4.8)$ & $29.6\pm9.3(2.9)$ \\
 & MWM & 8 & 40 & -- & $[{-},{100}]$ & -- & $50.5\pm11.9(3.8)$ & $30.9\pm7.3(2.3)$ \\
 & MWM & 8 & 60 & -- & $[{-},{100}]$ & -- & $58.7\pm15.2(4.8)$ & $36.0\pm9.3(2.9)$ \\
 & MWM & 8 & 5 & -- & $[{-},{80}]$ & -- & $48.3\pm15.2(4.8)$ & $29.6\pm9.3(2.9)$ \\
 & MWM$^\dagger$ & 8 & 5 & -- & $[{-},{100}]$ & -- & $47.9\pm15.2(4.8)$ & $29.4\pm9.3(2.9)$ \\
\midrule
%% -----------------------------------------------
%% ET
%% -----------------------------------------------
ET & MWM & 8 & 2 & -- & $[{-},{100}]$ & $10.6\pm0.7(0.2)^\star$ & $1.96\pm0.44(0.14)$ & $1.13\pm0.26(0.08)$ \\
 & MWM & 4 & 2 & -- & $[{-},{100}]$ & -- & $1.87\pm0.44(0.14)$ & $1.08\pm0.25(0.08)$ \\
 & MWM & 16 & 2 & -- & $[{-},{100}]$ & -- & $2.00\pm0.46(0.15)$ & $1.15\pm0.26(0.08)$ \\
 & MWM & 8 & 5 & -- & $[{-},{100}]$ & -- & $1.98\pm0.45(0.14)$ & $1.14\pm0.26(0.08)$ \\
 & MWM & 8 & 20 & -- & $[{-},{100}]$ & -- & $2.46\pm0.85(0.27)$ & $1.42\pm0.49(0.15)$ \\
 & MWM & 8 & 40 & -- & $[{-},{100}]$ & -- & $2.60\pm0.77(0.24)$ & $1.50\pm0.44(0.14)$ \\
 & MWM & 8 & 2 & -- & $[{-},{80}]$ & -- & $1.96\pm0.44(0.14)$ & $1.13\pm0.26(0.08)$ \\
 & MWM$^\dagger$ & 8 & 2 & -- & $[{-},{100}]$ & -- & $1.95\pm0.44(0.14)$ & $1.13\pm0.25(0.08)$ \\
\midrule
%% -----------------------------------------------
%% CE
%% -----------------------------------------------
CE & MWM & 8 & 2 & -- & $[{-},{100}]$ & $5.31\pm0.58(0.18)^\star$ & $1.30\pm0.41(0.13)$ & $0.751\pm0.239(0.075)$ \\
 & MWM & 4 & 2 & -- & $[{-},{100}]$ & -- & $1.29\pm0.40(0.13)$ & $0.746\pm0.232(0.073)$ \\
 & MWM & 16 & 2 & -- & $[{-},{100}]$ & -- & $1.30\pm0.41(0.13)$ & $0.752\pm0.239(0.075)$ \\
 & MWM & 8 & 5 & -- & $[{-},{100}]$ & -- & $1.30\pm0.41(0.13)$ & $0.751\pm0.239(0.075)$ \\
 & MWM & 8 & 20 & -- & $[{-},{100}]$ & -- & $1.43\pm0.46(0.14)$ & $0.825\pm0.263(0.083)$ \\
 & MWM & 8 & 40 & -- & $[{-},{100}]$ & -- & $1.74\pm0.41(0.13)$ & $1.01\pm0.23(0.07)$ \\
 & MWM & 8 & 2 & -- & $[{-},{80}]$ & -- & $1.30\pm0.42(0.13)$ & $0.749\pm0.241(0.076)$ \\
 & MWM$^\dagger$ & 8 & 2 & -- & $[{-},{100}]$ & -- & $1.29\pm0.41(0.13)$ & $0.747\pm0.236(0.075)$ \\
\midrule
%% -----------------------------------------------
%% ET+CE
%% -----------------------------------------------
ET$+$CE & MWM & 8 & 2 & -- & $[{-},{100}]$ & $4.74\pm0.45(0.14)^\star$ & $1.36\pm0.37(0.12)$ & $0.784\pm0.216(0.068)$ \\
 & MWM & 4 & 2 & -- & $[{-},{100}]$ & -- & $1.36\pm0.37(0.12)$ & $0.784\pm0.216(0.068)$ \\
 & MWM & 16 & 2 & -- & $[{-},{100}]$ & -- & $1.38\pm0.36(0.11)$ & $0.797\pm0.210(0.066)$ \\
 & MWM & 8 & 5 & -- & $[{-},{100}]$ & -- & $1.36\pm0.38(0.12)$ & $0.785\pm0.217(0.069)$ \\
 & MWM & 8 & 20 & -- & $[{-},{100}]$ & -- & $1.55\pm0.45(0.14)$ & $0.893\pm0.259(0.082)$ \\
 & MWM & 8 & 40 & -- & $[{-},{100}]$ & -- & $1.94\pm0.58(0.18)$ & $1.12\pm0.33(0.11)$ \\
 & MWM & 8 & 2 & -- & $[{-},{80}]$ & -- & $1.35\pm0.38(0.12)$ & $0.782\pm0.218(0.069)$ \\
 & MWM$^\dagger$ & 8 & 2 & -- & $[{-},{100}]$ & -- & $1.35\pm0.37(0.12)$ & $0.780\pm0.213(0.067)$ \\
\midrule
%% -----------------------------------------------
%% LISA (light seeds)
%% -----------------------------------------------
LISA-L & MWM & -- & -- & 16384 & $[{10^{4}},{10^{6}}]$ & -- & $175.5\pm74.7(23.6)$ & $55.5\pm23.6(7.5)$ \\
 & MWM & -- & -- & 4096 & $[{10^{4}},{10^{6}}]$ & -- & $174.5\pm74.1(23.4)$ & $55.2\pm23.4(7.4)$ \\
 & MWM & -- & -- & 8192 & $[{10^{4}},{10^{6}}]$ & -- & $175.1\pm73.7(23.3)$ & $55.4\pm23.3(7.4)$ \\
 & MWM$^\dagger$ & -- & -- & 16384 & $[{10^{4}},{10^{6}}]$ & -- & $164.0\pm68.1(21.5)$ & $51.9\pm21.5(6.8)$ \\
\midrule
%% -----------------------------------------------
%% LISA (heavy seeds)
%% -----------------------------------------------
LISA-H & MWM & -- & -- & 16384 & $[{10^{6}},{10^{8}}]$ & -- & $107.7\pm74.8(23.7)$ & $53.8\pm37.4(11.8)$ \\
 & MWM & -- & -- & 4096 & $[{10^{6}},{10^{8}}]$ & -- & $15.4\pm17.1(5.4)$ & $7.71\pm8.54(2.70)$ \\
 & MWM & -- & -- & 8192 & $[{10^{6}},{10^{8}}]$ & -- & $38.3\pm46.0(14.5)$ & $19.2\pm23.0(7.3)$ \\
 & MWM$^\dagger$ & -- & -- & 16384 & $[{10^{6}},{10^{8}}]$ & -- & $103.1\pm65.1(20.6)$ & $51.5\pm32.5(10.3)$ \\
 & NRSur & -- & -- & 16384 & $[{10^{6}},{10^{8}}]$ & -- & $82.2\pm69.1(21.8)$ & $41.1\pm34.5(10.9)$ \\
\bottomrule
\end{tabular}
}% end \small
\begin{minipage}{\linewidth}
\smallskip\footnotesize
$^\dagger$~MWM with NRSur7dq2 prior bounds ($q\!\geq\!0.5$, $|\chi|\!\leq\!0.8$).
$^\star$~Direct Fisher result at $d_L\!\leq\!700$\,Mpc ($N\!=\!100$); no $\sqrt{N}$ extrapolation.
$^\ddagger$~LISA uses SFR-like prior ($\alpha\!=\!2.7$); true SMBHB rate evolution poorly constrained.
$N_{\rm lo}\!=\!5$, $N_{\rm hi}\!=\!50$ total LISA events over the mission.
A dash (--) in the $M$ range lower bound indicates the ground-based default with no lower cut applied.
\end{minipage}
\end{table*}