% 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 & -- & $[{-},{100}]$ & $400.3\pm32.3(10.2)^\star$ & $100.4\pm41.2(13.0)$ & $61.5\pm25.2(8.0)$ \\
 & MWM & 4 & 5 & -- & $[{-},{100}]$ & -- & $100.7\pm41.5(13.1)$ & $61.7\pm25.4(8.0)$ \\
 & MWM & 16 & 5 & -- & $[{-},{100}]$ & -- & $101.8\pm40.5(12.8)$ & $62.3\pm24.8(7.8)$ \\
 & 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 & -- & $[{-},{100}]$ & -- & $142.2\pm35.4(11.2)$ & $87.1\pm21.7(6.9)$ \\
 & MWM & 8 & 5 & -- & $[{-},{80}]$ & -- & $100.5\pm41.2(13.0)$ & $61.6\pm25.3(8.0)$ \\
 & MWM$^\dagger$ & 8 & 5 & -- & $[{-},{100}]$ & -- & $99.3\pm40.9(12.9)$ & $60.8\pm25.0(7.9)$ \\
\midrule
%% -----------------------------------------------
%% ET
%% -----------------------------------------------
ET & MWM & 8 & 2 & -- & $[{-},{100}]$ & $26.1\pm1.6(0.5)^\star$ & $1.71\pm0.33(0.11)$ & $0.987\pm0.192(0.061)$ \\
 & MWM & 4 & 2 & -- & $[{-},{100}]$ & -- & $1.69\pm0.36(0.11)$ & $0.974\pm0.206(0.065)$ \\
 & MWM & 16 & 2 & -- & $[{-},{100}]$ & -- & $1.76\pm0.32(0.10)$ & $1.02\pm0.18(0.06)$ \\
 & MWM & 8 & 5 & -- & $[{-},{100}]$ & -- & $1.73\pm0.34(0.11)$ & $1.00\pm0.19(0.06)$ \\
 & MWM & 8 & 20 & -- & $[{-},{100}]$ & -- & $2.87\pm0.54(0.17)$ & $1.66\pm0.31(0.10)$ \\
 & MWM & 8 & 40 & -- & $[{-},{100}]$ & -- & $3.34\pm0.62(0.20)$ & $1.93\pm0.36(0.11)$ \\
 & MWM & 8 & 2 & -- & $[{-},{80}]$ & -- & $1.72\pm0.33(0.10)$ & $0.990\pm0.191(0.060)$ \\
 & MWM$^\dagger$ & 8 & 2 & -- & $[{-},{100}]$ & -- & $1.70\pm0.32(0.10)$ & $0.982\pm0.187(0.059)$ \\
\midrule
%% -----------------------------------------------
%% CE
%% -----------------------------------------------
CE & MWM & 8 & 2 & -- & $[{-},{100}]$ & $13.2\pm1.3(0.4)^\star$ & $1.06\pm0.30(0.09)$ & $0.613\pm0.172(0.054)$ \\
 & MWM & 4 & 2 & -- & $[{-},{100}]$ & -- & $1.04\pm0.26(0.08)$ & $0.600\pm0.152(0.048)$ \\
 & MWM & 16 & 2 & -- & $[{-},{100}]$ & -- & $1.06\pm0.30(0.09)$ & $0.614\pm0.172(0.054)$ \\
 & MWM & 8 & 5 & -- & $[{-},{100}]$ & -- & $1.06\pm0.30(0.09)$ & $0.613\pm0.172(0.054)$ \\
 & 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 & -- & $[{-},{100}]$ & $11.7\pm1.0(0.3)^\star$ & $1.11\pm0.28(0.09)$ & $0.643\pm0.161(0.051)$ \\
 & MWM & 4 & 2 & -- & $[{-},{100}]$ & -- & $1.11\pm0.28(0.09)$ & $0.640\pm0.163(0.052)$ \\
 & MWM & 16 & 2 & -- & $[{-},{100}]$ & -- & $1.12\pm0.27(0.09)$ & $0.646\pm0.157(0.050)$ \\
 & 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 & -- & -- & 16384 & $[{10^{4}},{10^{6}}]$ & -- & $360.8\pm151.2(47.8)$ & $80.7\pm33.8(10.7)$ \\
 & MWM & -- & -- & 4096 & $[{10^{4}},{10^{6}}]$ & -- & $360.3\pm151.0(47.7)$ & $80.6\pm33.8(10.7)$ \\
 & MWM & -- & -- & 8192 & $[{10^{4}},{10^{6}}]$ & -- & $360.4\pm150.9(47.7)$ & $80.6\pm33.7(10.7)$ \\
 & MWM$^\dagger$ & -- & -- & 16384 & $[{10^{4}},{10^{6}}]$ & -- & $302.1\pm106.4(33.6)$ & $67.6\pm23.8(7.5)$ \\
\midrule
%% -----------------------------------------------
%% LISA (heavy seeds)
%% -----------------------------------------------
LISA-H & MWM & -- & -- & 16384 & $[{10^{6}},{10^{8}}]$ & -- & $480.5\pm260.0(82.2)$ & $151.9\pm82.2(26.0)$ \\
 & MWM & -- & -- & 4096 & $[{10^{6}},{10^{8}}]$ & -- & $534.7\pm293.6(92.8)$ & $169.1\pm92.8(29.4)$ \\
 & MWM & -- & -- & 8192 & $[{10^{6}},{10^{8}}]$ & -- & $522.2\pm325.8(103.0)$ & $165.1\pm103.0(32.6)$ \\
 & MWM$^\dagger$ & -- & -- & 16384 & $[{10^{6}},{10^{8}}]$ & -- & $461.5\pm269.1(85.1)$ & $145.9\pm85.1(26.9)$ \\
\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*}