Interior Generation of a Static VGM Response Amplitude: Regular Central Solutions, Dependency-Preserving Constitutive Closure, and Exterior Matching

This work develops an interior completion of the static spherical VGM response problem by examining how a regular matter configuration can generate the exterior response amplitude while preserving the Organizational Field Theory dependency order Ω→κ→Φμ→Ψν\Omega \rightarrow \kappa \rightarrow \Phi^\mu \rightarrow \Psi^\nu. An explicit reduced realization is constructed from an isentropic barotropic fluid, a canonical massive covector, and a dependency-derived source weight. The analysis derives the constrained variational structure, exact spherical field equations, regular central expansions, free-data count, continuation conditions, surface and junction relations, and the matching map connecting regular interior data to the exterior amplitude qAq_A. A Green-identity representation and a closed-form constant-density weak-field solution demonstrate that the admissible interior-to-exterior source map is nonempty. Universal couplings are distinguished from source-dependent integration data, and a dimensionless nonlinear boundary-value formulation is provided for further model-specific analysis. The result constitutes a conditional interior completion of the VGM static forward problem, subject to explicit correspondence, stability, validation, identifiability, and falsifiability requirements. It is presented as a mathematically controlled constitutive realization, not as observational evidence for new physics or as a unique final VGM constitutive law.