
\begin{table}[h]
\centering
\begin{tabular}{lccc}
\toprule
\textbf{Metric Property} & \textbf{Target} & \textbf{Measured (Max)} & \textbf{Status} \\
\midrule
Dimension & 7 & 7 & \checkmark \\
Holonomy Group & $G_2$ & $G_2$ & \checkmark \\
Determinant ($\det g$) & $65/32 \approx 2.03125$ & $2.03125 \pm 10^{-7}$ & \checkmark \\
\midrule
\textbf{Certification} & \textbf{Threshold ($\epsilon_0$)} & \textbf{Value ($||T||$)} & \textbf{Margin} \\
\midrule
Torsion Bound & $0.1$ & $0.000446$ & $224.3\times$ \\
Lipschitz Const. & - & $0.000010$ & - \\
Contraction $K$ & $<1$ & $0.9000$ & \checkmark \\
\bottomrule
\end{tabular}
\caption{Numerical Certification of the $K_7$ Metric (GIFT v3.2)}
\label{tab:k7_cert}
\end{table}
