Abstract We analyze the interior inertial-density field equation derived from the IGT Lagrangian under spherical symmetry with regular boundary conditions at the origin. A near-origin expansion yields a locally regular solution ρᵢ(r) = ρ₀ + O(r2), with ρᵢ finite and ρᵢ′(0) = 0. If the effective gravitating density is a smooth function of ρᵢ, then Menc(r) ∼ r³ and α loc(r) = 2 G Menc(r) /(r c²) ∼ r² → 0 as r → 0. Power-law divergent branches require non-regular boundary conditions or non-generic large-field growth of V′(ρᵢ). Under smooth potentials and regular origin data, the admissible interior solutions exhibit a finite structure. Notably, the resulting finite-core scaling Menc(r) ∼ r³ (and hence α loc(r) ∼ r²) matches the regular-core behavior often associated with “de Sitter–like” interiors in the regular–black-hole literature (Bardeen, 1968; Dymnikova, 1992; Hayward, 2006; Ansoldi, 2008), but here it arises directly from the IGT inertial-density field equation under mild smoothness and regularity assumptions rather than being imposed as an ansatz.