Wronskian correction to MOND from the geometric relay: empirical test on 174 SPARC galaxies

This record presents an empirical test of a Wronskian correction to the MOND interpolation function derived from the Geometric Relay Theory (GRT), itself built upon Minazzoli’s Entangled Relativity framework. The proposed correction replaces the fixed Milgrom acceleration scale by an effective radial acceleration scale, controlled by an integrated baryonic desynchronisation variable built from the stellar and gas contributions to the rotation curve. The model is tested on 174 galaxies from the SPARC catalogue using three frozen global parameters selected by 5-fold cross-validation: kappa = 5, epsilon = 0.2, and alpha = 0.5. With no per-galaxy adjustment, the corrected model improves over standard MOND for 111 out of 174 galaxies, corresponding to a win rate of 63.8%, with a 95% bootstrap confidence interval of 57% to 70%. The improvement is strongest for dwarf galaxies, with a win rate of 75.6%, and disappears for the most massive spirals, consistent with the theoretical expectation that the Wronskian correction should extinguish in the deep Newtonian or baryon-concentrated regime. The mean relative gain is approximately +3.0%, and a permutation test gives p < 0.001. The correction is also reported as robust against the McGaugh radial acceleration relation, with a mean relative gain of +2.91% when compared to the RAR prediction. These results do not claim to replace MOND or dark matter models. They show that a theoretically motivated, minimal Wronskian correction derived from a scalar-tensor relay framework produces a statistically significant and structurally coherent improvement on SPARC rotation curves. The decisive next test is the application of the same frozen model to the forthcoming BIG-SPARC sample.