Discrete Coupling Levels in Galaxy Rotation-Curve Fits from a Baryonic Field Proxy (SPARC)

We present a strictly empirical test on the SPARC rotation-curve catalog using a minimal centrally sourced contribution modeled by an exponential radial attenuation kernel, modulated by a baryon-dependent saturation factor. The additional term is implemented directly at the velocity level (combined in quadrature with the visible-only baseline), yielding a compact phenomenological model applicable across a heterogeneous galaxy sample. We apply the same fixed functional form and global parameters uniformly across the catalog (in this analysis, N=175 usable systems) and evaluate the resulting fits using per-galaxy diagnostics including RMSE, correlations, reduced chi² with a fixed velocity jitter, and standardized residual measures. Using this uniform empirical rule, we obtain strong global agreement for a substantial fraction of the sample, with a median Pearson correlation of 0. 96 between Vₒbs and Vₘodel prior to incorporating measurement uncertainties. The outcomes are not unambiguous. Alongside the strong correlations and many visually coherent reconstructions, a non-negligible subset of galaxies behave as clear outliers, and these failures are discussed explicitly. We interpret this mixed performance conservatively as raising questions about the appropriate domain of validity of one-dimensional rotation-curve modeling within SPARC and the extent to which a single 1D proxy can capture intrinsically complex galactic dynamics.