% 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
%% -----------------------------------------------
%% LISA (light seeds)
%% -----------------------------------------------
LISA-L & MWM$^\dagger$ & -- & -- & 16384 & $[{10^{4}},{10^{6}}]$ & -- & $911.0\pm309.6(138.5)$ & $203.7\pm69.2(31.0)$ \\
 & MWM$^\dagger$ & -- & -- & 65536 & $[{10^{4}},{10^{6}}]$ & -- & $922.0\pm358.7(160.4)$ & $206.2\pm80.2(35.9)$ \\
\midrule
%% -----------------------------------------------
%% LISA (heavy seeds)
%% -----------------------------------------------
LISA-H & MWM$^\dagger$ & -- & -- & 16384 & $[{10^{6}},{10^{8}}]$ & -- & -- & -- \\
 & MWM$^\dagger$ & -- & -- & 65536 & $[{10^{6}},{10^{8}}]$ & -- & -- & -- \\
\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*}