An Identifiability Audit of One-Parameter Structural Corrections to the Radial Acceleration Relation in SPARC

Abstract

We ask whether any one-parameter structural correction to the radial acceleration relation (RAR) can be uniquely recovered from SPARC rotation curves, and answer with an identifiability audit: each candidate is benchmarked against per-galaxy nuisance freedom, with predictive scoring against mass-only and data-quality baselines. In the full sample (N = 126) the answer is no: a hybrid compactness term improves the fit, but zero-point freedom absorbs the gain, and in cross-validation the model fails to out-predict a mass-only baseline and loses to a quality-flag baseline. One regime retains structural information: in gas-dominated, low-acceleration disks -- where MOND's strict locality and $\Lambda$CDM feedback models diverge most sharply -- the RAR residual correlates with compactness ($r=0.46$, $p=1.3\times10^{-4}$), remains significant under hierarchical partial pooling ($\beta=0.23$, $p=1.7\times10^{-5}$; N = 63), and survives canonical joint control for quality, sampling, mass, inclination error, and first-order pressure support ($r=0.30$, $p=0.02$). All significant results pass a Benjamini-Hochberg correction over the declared 27-test family. Three limits temper that survival: it is not significant under rank-based control over the widest proxy set; it resides in faint dwarfs independent surveys do not reach; and after mass control it is shared across the mass-size manifold. Pressure support brackets the interpretation -- isotropic drift correction absorbs a quarter of the amplitude, while a Jeans treatment overcorrects resolved cases -- leaving the physical origin undetermined. The audit's product is the extraction limit: claimed corrections must clear the 0.106 dex per-galaxy nuisance floor, a mass-only baseline, and data-quality stratification.