What does this equation mean?

Even a network that has cleared every check above owes one more: any fictitious, non-curvature contribution to a naive second difference has to be ruled out on its own terms, not merely assumed absent. A uniformly rotating platform’s centrifugal potential, -$\tfrac12$|$\boldsymbol\Omega$$\times$$\mathbf r$|^2 , has a nonzero Hessian too — for rotation about the z -axis, $\mathrm{diag}(-\Omega^2,-\Omega^2,0)$ — but that Hessian is exactly constant across any laboratory-scale network, tied to a rotation axis independently known from astrometry to extraordinary precision, and entirely absent from the trace-free, 2:{-1}:{-1} , 1/$r^3$ -falling pattern a genuine point-like or spherical mass produces. A real curvature signal has to fall as the network’s baseline moves farther from the source, has to keep its stretching axis pointed at the local vertical as the network is relocated, and has to hold the exact 2:{-1}:{-1} eigenvalue ratio once any independently known rotational or accelerated-frame contribution has been subtracted using its own, separately measured parameters — never fitted freely alongside the curvature term, which would let the two masquerade as each other.