% 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
HLV & $160.3\pm12.8$ & $48.3\pm15.2$ & $29.6\pm9.3$ \\
ET & $10.6\pm0.7$ & $1.96\pm0.44$ & $1.13\pm0.26$ \\
CE & $5.31\pm0.58$ & $1.30\pm0.41$ & $0.751\pm0.239$ \\
ET$+$CE & $4.74\pm0.45$ & $1.36\pm0.37$ & $0.784\pm0.216$ \\
LISA (heavy)$^\dagger$ & --- & $107.7\pm74.8$ & $53.8\pm37.4$ \\
LISA (light)$^\dagger$ & --- & $175.5\pm74.7$ & $55.5\pm23.6$ \\
\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}