Galactic Rotation Curves from a Universal Energy-Field Velocity Profile

We present a systematic statistical analysis of galactic rotation curves within the framework of Source Energy Field Theory (SEFT), using the full SPARC sample of 175 disk galaxies. Motivated by the weak-field asymptotic structure of SEFT, we construct a globally constrained Padé–logarithmic baseline velocity profile, whose universal parameters are determined once through robust global optimization and held fixed throughout a hierarchical galaxy-by-galaxy fitting procedure. Each galaxy is analyzed using a conservative two-stage model-selection procedure: a baseline model is adopted unless χ²_red ≥ 2, in which case compact nonlinear (Case A) or central steepening (Case B) corrections are introduced only under strong information-criterion support (ΔAICc_ext ≤ −10). Within this framework, 68.6% of galaxies are statistically well described by the universal baseline, while 20.6% and 10.9% require Case A and Case B corrections, respectively. Direct AICc-based comparisons with baryon + NFW ΛCDM models yield median ΔAICc_Λ = +6.53 (fixed-Υ, k=4, N=165), +13.18 (free-Υ, k=6, N=143), and +3.98 (Planck-virial constrained, k=2, N=175). Five-fold cross-validation yields a positive median ΔAICc_Λ = +1.88, and nonparametric bootstrap confirms the stability of the hierarchical classification. These results suggest that a globally constrained analytic velocity profile provides a statistically competitive and structurally coherent description of galactic rotation curves within a conservative hierarchical model-selection framework.