% Table 1: Summary H0 precision — Fisher direct and projected, no Bayesian projections
\begin{table}[t]
\centering
\caption{Fisher $1\sigma$ uncertainty on $H_0$ [$\kms$] from GW memory for each detector
configuration. \emph{Direct} ($N\!=\!100^\star$) is the Fisher result from $\sim\!100$ events
at $d_L\!\leq\!700$\,Mpc. \emph{Projected} columns give Fisher-ratio extrapolations
via Eq.~(\ref{eq:extrap}) for conservative ($N_{\rm lo}$) and optimistic ($N_{\rm hi}$)
event totals from Table~\ref{tab:rates}. All values use MWM. LISA values are
Fisher-only; see Appendix~\ref{app:full_table} for the full OAT scan.}
\label{tab:main_results}
\setlength{\tabcolsep}{4pt}
\begin{tabular}{lccc}
\toprule
Detector & $\sH^{\rm Fish\star}$ & $N_{\rm lo}$ & $N_{\rm hi}$ \\
\midrule
LISA (heavy)$^\dagger$ & --- & --- & --- \\
LISA (light)$^\dagger$ & --- & $810.2$ & $181.2$ \\
\bottomrule
\end{tabular}
\begin{minipage}{\columnwidth}
\smallskip\footnotesize
$^\star$ Direct Fisher result at $d_L\!\leq\!700$\,Mpc ($N\!=\!100$ events);
no $\sqrt{N}$ extrapolation applied. Population scatter quoted as $\pm$ values.
$^\dagger$ LISA projections use SFR-like prior ($\alpha\!=\!2.7$); the true
SMBHB rate evolution is poorly constrained.
\end{minipage}
\end{table}