Constraint-Driven Formation of Coherence Structures and Their Inverse-Square Exterior Flux

This paper investigates a coherence-driven mechanism for generating the inverse-square scaling behavior commonly associated with galactic rotation curves and gravitational lensing. Within the framework of Coherence Geometry, constrained variational-relaxation dynamics generate stable coherence basins corresponding to local minima of an intrinsic structure functional. When realized in spatially extended systems, these basins form curvature-confined structures whose exterior dynamics satisfy flux conservation. The resulting exterior flux exhibits inverse-square scaling, producing an effective density profile rho(r) ~ r^-2. This profile reproduces the leading-order gravitational signatures examined in the preceding papers on galactic rotation curves and gravitational lensing. The paper establishes a dynamical chain connecting coherence dynamics, structure formation, conserved exterior flux, inverse-square density scaling, and observable gravitational behavior. In this framework, inverse-square scaling is not prescribed in advance but emerges as a consequence of coherence-driven structure formation together with flux conservation in the exterior region. This paper forms the third part of a three-paper sequence on conserved flux, inverse-square density profiles, gravitational lensing, and coherence-driven structure formation. This document is released as part of the public Coherence Geometry research corpus.