What does this equation mean?

Define the network’s curvature-diagnosing observable directly from this result, restoring physical units through the relation between coordinate acceleration and proper time for a static observer, $\mathcal T_{ij} := c^2\left(\phi_{,ij} + \phi_{,i}\,\phi_{,j}\right)$. a symmetric rank-two tensor in the local spatial frame of the static observers, with units of inverse time squared — the Eötvös units already standard in gravity-gradient surveying, where 1\,$\mathrm E$ = 10^{-9}\,$\mathrm{s^{-2}}$ . Under a rotation of the local spatial axes it transforms as an ordinary rank-two tensor; under a change of which node is used as the additive reference for $\phi$ it is unchanged, because it depends only on derivatives of $\phi$ , never its value; and up to the factor $U^2$ $\approx$ 1 negligible at the one-part-in- 10^9 level for any terrestrial network, it is $c^2$ times the frame component $R^i${}_{0j0} of the Riemann tensor in the static observers’ own rest frame — a genuine curvature quantity, reported honestly as one stated-frame component rather than a coordinate-free scalar invariant, exactly the caveat this construction owes a reader.