Conserved Flux and Inverse-Square Density Profiles in Galactic Rotation Curves

This paper presents a flux-conservation mechanism for the inverse-square density scaling commonly associated with galactic dark matter halos. The central result is that conserved outward energy flux in the exterior region of a localized field configuration naturally implies an effective density profile rho(r) ~ r^-2. This profile gives an enclosed effective mass M(r) ~ r and therefore produces approximately flat galactic rotation curves. The derivation uses standard field-theoretic ingredients, including conservation of a Noether energy flux in a source-free exterior region. No additional particle sector, modified gravitational law, or prescribed halo profile is assumed. This paper is the first part of a sequence on conserved flux, inverse-square density profiles, gravitational lensing, and coherence-driven structure formation. It is intended to isolate the scaling mechanism itself before later work examines lensing behavior and possible Coherence Geometry sources for the conserved exterior flux. This document is released as part of the public Coherence Geometry research corpus.