A Coherence–Topology Invariant Governing Non-Local Gravitational Response

We introduce a dimensionless invariant that characterizes the radial extent of non-local gravitational response in disk galaxies, derived directly from the morphology of neutral hydrogen (HI) distributions. The invariant \eta = R_{\mathrm{trans}} / R_{\mathrm{flux}} measures the transition scale of the predicted radial acceleration profile relative to the baryonic disk size.

The gravitational response is computed by solving a non-local Helmholtz equation with a source field constructed from observed HI surface density, without invoking dark matter halos, empirical force laws, or rotation-curve fitting. Across a sample of 15 galaxies, the resulting response profiles exhibit a tight homology when expressed in normalized coordinates. The propagation extent \eta varies monotonically with a coherence economy invariant but is gated by a separate topological connectivity threshold, indicating that coherence alone is necessary but not sufficient for extended propagation.

The framework is explicitly falsifiable and demonstrates stability under domain variation. Preliminary stress tests using SPARC baryonic profiles indicate robustness under projection to one-dimensional data, motivating further large-sample studies.