An effective relational dynamical model for galaxy rotation curves: tests with the SPARC dataset

We test an effective, regime-dependent relational dynamics (MEI) against the SPARC database of 175 disk galaxies, which provides high-quality HI/H$\alpha$ rotation curves and homogeneous baryonic mass models derived from Spitzer 3.6,$\mu$m photometry. The model is formulated as an effective acceleration law sourced by the observed baryonic distribution and constructed to recover the Newtonian limit in the inner, high-acceleration regime. Using standard SPARC quality cuts and a fixed set of global model hyperparameters, we compare predicted and observed rotation curves across the sample, perform residual diagnostics as a function of radius and galaxy properties, and assess the stability of global performance via galaxy-level bootstrap resampling. We find that the MEI effective law reproduces the main diversity of SPARC rotation-curve shapes without invoking non-baryonic dark matter halos and achieves performance competitive with standard MOND fits under comparable assumptions, while introducing a structurally distinct transition mechanism tied to galaxy size rather than to a universal acceleration threshold. We emphasize the effective character and limited scope of the model: it is presented as a galactic-scale dynamical correction operating in quasi-stationary disk systems, not as a fundamental modification of gravity nor as a claim of immediate extrapolation to clusters or cosmology. The present analysis therefore constitutes a first empirical step within a broader research programme aimed at testing whether analogous regime-dependent dynamical structures can be consistently identified across other physical domains, including cosmological background evolution, linear structure growth, and nonlinear plasma dynamics.