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

We introduce and test an effective regime-dependent dynamical framework (Modular Effective Interaction, MEI) against the SPARC database of 175 disk galaxies, which provides high-quality HI/Hα rotation curves and homogeneous baryonic mass models derived from Spitzer 3.6 μm photometry. The model introduces a structural transition scale r0 = 40.5 Rd tied to the exponential disk scale length and a global amplitude parameter alpha, interpreted as an effective regime-dependent correction to the baryonic contribution, without invoking non-baryonic dark matter components or modifying the gravitational sector. In the baseline, alpha is determined from a single global optimisation over the full sample; a homogeneous galaxy-by-galaxy refit is performed separately to characterise the population-level distribution of best-fit parameters. Applying standard SPARC quality cuts (Q ≤ 2, G = 163 galaxies), MEI achieves a reduced chi-squared of 1.05 and an RMS of 6.3 km/s across the full sample, compared to a reduced chi-squared of 1.28 for MOND and 6.84 for Newtonian baryons-only dynamics under comparable parametric assumptions. Bootstrap resampling confirms the statistical robustness of these results. A central new result emerges from the galaxy-by-galaxy refit: the best-fit amplitude alpha correlates significantly with the disk scale length Rd (alpha proportional to Rd^1.11, r = 0.754, p < 1e-24). Crucially, the partial correlation controlling for the stellar mass-to-light ratio strengthens rather than weakens this relation (r_partial = 0.773, p < 1e-26), demonstrating that disk size carries independent structural information beyond the baryonic mass budget. This result constitutes a qualitative discriminant between MEI and acceleration-threshold frameworks such as MOND: the relevant dynamical scale is structural, not kinematic. The framework is presented as an effective description valid for quasi-stationary disk systems. Its extension to additional physical regimes is the subject of ongoing work.