% 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 & $400.3\pm32.3$ & $100.4\pm41.2$ & $61.5\pm25.2$ \\
ET & $26.1\pm1.6$ & $1.71\pm0.33$ & $0.987\pm0.192$ \\
CE & $13.2\pm1.3$ & $1.06\pm0.30$ & $0.613\pm0.172$ \\
ET$+$CE & $11.7\pm1.0$ & $1.11\pm0.28$ & $0.643\pm0.161$ \\
LISA (heavy)$^\dagger$ & --- & $480.5\pm260.0$ & $151.9\pm82.2$ \\
LISA (light)$^\dagger$ & --- & $360.8\pm151.2$ & $80.7\pm33.8$ \\
\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}