Phenomenological Analysis of the Adiabatic Geometric Leveling Eective Field Theory on the SPARC Rotation Curve Catalog

We present a systematic phenomenological analysis of an eective eld theory (EFT)extension of the Adiabatic Geometric Leveling (AGL) model applied to galactic rotationcurves from the SPARC catalog (N = 175 galaxies). The AGL-EFT introduces two param-eters: a coupling constant Λobs and a range scale α, correcting the circular velocity prolethrough the kernel Galt(R, α) = (1−e−R/α)/(R/α). We show that the previously used kernelGorig = 1 − e−R/α/(R/α) changes sign at R/α ≈ 0.567, introducing a systematic artifactthat forces 100% of solutions to the boundary of the parameter space. With the correctedkernel, 56.6% of galaxies yield identiable (interior) solutions. In the interior subsample(N = 99), a Wilcoxon signed-rank test conrms a statistically signicant reduction in χ2νrelative to the ISO baseline (W = 1173, p = 5.5 × 10−6). Under the Kass & Raftery (1995)evidence scale, 23.4% of the full sample shows strong evidence for AGL (∆AIC < −10).Critically, Λobs is consistent with zero mean (t-test p = 0.63, Wilcoxon p = 0.84) and showsno signicant degeneracy with α (Spearman ρ = 0.068, p = 0.51), conrming that the twoparameters are independently constrained. We also report that ∆AIC correlates signicantlywith the number of data points (ρ = −0.47, p < 10−4), which we discuss as a limitationof the analysis. We identify DDO154 as a case study with a genuine interior minimum atΛobs = 1.67, demonstrating parameter identiability in at least a subset of the sample.