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, defined as the ratio of a transition radius to the enclosed-flux radius of the baryonic disk, measures the scale at which the predicted radial acceleration profile transitions from an inner to an outer regime. The gravitational response is computed by solving a non-local Helmholtz equation with a source field constructed from the 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 varies monotonically with a coherence-economy invariant that quantifies the balance between supported curvature capacity and structural fragmentation, but extended propagation occurs only when a separate topological connectivity measure exceeds a threshold value. This indicates that coherence alone is necessary but not sufficient for extended gravitational response. The framework is explicitly falsifiable and demonstrates stability under variation of disk boundaries. Preliminary stress tests using SPARC baryonic profiles indicate robustness under projection to one-dimensional data, motivating further large-sample studies.