Phenomenology of the anomalous acceleration in SPARC galaxies: A disk-scaled profile with zero local free parameters

An empirical radial profile for the anomalous (non-baryonic) velocity component in spiral galaxy rotation curves is presented, motivated by extended gravity considerations but validated independently of any specific theoretical framework. The profile takes the form Vₐₙₒₘ²(r) = C₀ · (r/2Rscale) · exp(-r/12Rscale), where Rscale is a mass-weighted hybrid baryonic scale length and C₀ is a dimensional screening constant predicted from the total baryonic mass. The model relies exclusively on 4 global constants (2 radial, 2 regression) and features zero local free parameters per galaxy, maintaining theoretical independence from MOND's acceleration scale (a₀). The unconstrained regression empirically recovers a scaling relation (Vₐₙₒₘ ∝ Mbar0.243) consistent with the Baryonic Tully-Fisher proportionality. Applied to 174 galaxies from the SPARC database (3,391 rotation curve data points), the model achieves a median error of 11.7% across the combined sample. Under identical zero-local-parameter conditions, the model yields tighter residuals than MOND applied via the Radial Acceleration Relation (RAR) overall (22.8%). Residual analysis shows no significant correlation with any observable galaxy property. By generalising from the stellar disk to the total baryonic disk via the empirical HI size-mass relation (Wang et al. 2016), the profile prevents unphysical divergence in extreme gas-dominated dwarfs. Dataset and Reproduction Code: https://doi.org/10.5281/zenodo.20276507