Quadratic form and sign

A separate stationary normalization check agrees with attraction. With ${\kappa }^2=8\pi G_N$, a positive static density $\rho$ in the unswitched weak-field diagnostic gives

where ${\Phi }_N=-G_N\int \rho (y)/|\mathbf{x}-\mathbf{y}|{\mathrm{d}}^{3}y$. For the usual stationary nonrelativistic reduction, ${\gamma }_{00}=2{\Phi }_N$ and acceleration is $-\nabla {\Phi }_N$. This is a sign check on the frozen completion action, not a static solution produced by the compact-time experiment or a host update.