% 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 & 4 & 5 & -- & $[{-},{100}]$ & -- & $100.7\pm41.5(13.1)$ & $61.7\pm25.4(8.0)$ \\
 & MWM & 8 & 20 & -- & $[{-},{100}]$ & -- & $100.5\pm41.2(13.0)$ & $61.6\pm25.3(8.0)$ \\
 & MWM & 8 & 40 & -- & $[{-},{100}]$ & -- & $112.8\pm31.0(9.8)$ & $69.1\pm19.0(6.0)$ \\
 & MWM & 8 & 60 & -- & $[{-},{100}]$ & -- & $142.2\pm35.4(11.2)$ & $87.1\pm21.7(6.9)$ \\
\midrule
%% -----------------------------------------------
%% ET
%% -----------------------------------------------
ET & MWM & 4 & 2 & -- & $[{-},{100}]$ & -- & $1.69\pm0.36(0.11)$ & $0.974\pm0.206(0.065)$ \\
 & MWM & 8 & 20 & -- & $[{-},{100}]$ & -- & $2.87\pm0.54(0.17)$ & $1.66\pm0.31(0.10)$ \\
 & MWM & 8 & 40 & -- & $[{-},{100}]$ & -- & $3.34\pm0.62(0.20)$ & $1.93\pm0.36(0.11)$ \\
\midrule
%% -----------------------------------------------
%% CE
%% -----------------------------------------------
CE & MWM & 4 & 2 & -- & $[{-},{100}]$ & -- & $1.04\pm0.26(0.08)$ & $0.600\pm0.152(0.048)$ \\
 & MWM & 8 & 20 & -- & $[{-},{100}]$ & -- & $1.34\pm0.34(0.11)$ & $0.773\pm0.196(0.062)$ \\
 & MWM & 8 & 40 & -- & $[{-},{100}]$ & -- & $2.18\pm0.65(0.21)$ & $1.26\pm0.38(0.12)$ \\
 & MWM & 8 & 2 & -- & $[{-},{80}]$ & -- & $1.06\pm0.30(0.09)$ & $0.614\pm0.172(0.054)$ \\
 & MWM$^\dagger$ & 8 & 2 & -- & $[{-},{100}]$ & -- & $1.05\pm0.29(0.09)$ & $0.609\pm0.170(0.054)$ \\
\midrule
%% -----------------------------------------------
%% ET+CE
%% -----------------------------------------------
ET$+$CE & MWM & 8 & 2 & -- & $[{-},{100}]$ & -- & $1.11\pm0.28(0.09)$ & $0.643\pm0.161(0.051)$ \\
 & MWM & 4 & 2 & -- & $[{-},{100}]$ & -- & $1.11\pm0.28(0.09)$ & $0.640\pm0.163(0.052)$ \\
 & MWM & 8 & 5 & -- & $[{-},{100}]$ & -- & $1.12\pm0.28(0.09)$ & $0.645\pm0.162(0.051)$ \\
 & MWM & 8 & 20 & -- & $[{-},{100}]$ & -- & $1.52\pm0.38(0.12)$ & $0.879\pm0.220(0.070)$ \\
 & MWM & 8 & 40 & -- & $[{-},{100}]$ & -- & $2.30\pm0.56(0.18)$ & $1.33\pm0.32(0.10)$ \\
 & MWM & 8 & 2 & -- & $[{-},{80}]$ & -- & $1.11\pm0.28(0.09)$ & $0.643\pm0.161(0.051)$ \\
 & MWM$^\dagger$ & 8 & 2 & -- & $[{-},{100}]$ & -- & $1.11\pm0.28(0.09)$ & $0.638\pm0.159(0.050)$ \\
\midrule
%% -----------------------------------------------
%% LISA (light seeds)
%% -----------------------------------------------
LISA-L & MWM & -- & -- & 4096 & $[{10^{4}},{10^{6}}]$ & -- & $253.4\pm97.2(30.7)$ & $56.7\pm21.7(6.9)$ \\
 & MWM & -- & -- & 8192 & $[{10^{4}},{10^{6}}]$ & -- & $251.4\pm95.9(30.3)$ & $56.2\pm21.4(6.8)$ \\
 & MWM$^\dagger$ & -- & -- & 16384 & $[{10^{4}},{10^{6}}]$ & -- & $224.6\pm76.7(24.3)$ & $50.2\pm17.2(5.4)$ \\
\midrule
%% -----------------------------------------------
%% LISA (heavy seeds)
%% -----------------------------------------------
LISA-H & MWM & -- & -- & 16384 & $[{10^{6}},{10^{8}}]$ & -- & $231.1\pm72.9(23.0)$ & $73.1\pm23.0(7.3)$ \\
 & MWM & -- & -- & 4096 & $[{10^{6}},{10^{8}}]$ & -- & $250.2\pm81.4(25.7)$ & $79.1\pm25.7(8.1)$ \\
 & MWM & -- & -- & 8192 & $[{10^{6}},{10^{8}}]$ & -- & $232.7\pm73.8(23.3)$ & $73.6\pm23.3(7.4)$ \\
 & MWM$^\dagger$ & -- & -- & 16384 & $[{10^{6}},{10^{8}}]$ & -- & $210.6\pm63.7(20.1)$ & $66.6\pm20.1(6.4)$ \\
\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*}