Scalar Field Phase Transition and Galaxy Rotation Curves in a Covariant Framework

We construct a covariant scalar field model in which galaxy rotation curve anomalies arise from phase-transition dynamics of a unified scalar field. In the weak-field limit, gradient energy contributes an additional gravitational source term. An intrinsic acceleration scale a0 emerges from field parameters without phenomenological input.
Using 169 SPARC galaxies, we obtain a median RAR ratio of 1.001 with 0.147 dex scatter. The results suggest that galactic-scale gravitational anomalies can be understood as emergent behavior of scalar field phase transitions.