The Role of Surface-Brightness Coupling in Galaxy Rotation Curves: Evidence from the H₂ Descriptor in SPARC and LITTLE THINGS

This work investigates the role of a nonlinear baryonic structural descriptor defined as: H₂ = SB_disk × V_bar³ within galaxy rotation curve data from the SPARC (Lelli et al., 2016) and LITTLE THINGS datasets. The study evaluates whether surface-brightness coupling introduces statistically significant residual predictive information beyond standard baryonic scaling relations. A locked phenomenological framework is applied, including baseline baryonic modeling, BTFR redundancy control, cross-validation, bootstrap resampling, permutation testing, and halo-model comparisons (NFW, Einasto, DC14). The results indicate that the H₂ descriptor consistently improves rotation curve fits in dwarf and low surface-brightness galaxies, while maintaining low multicollinearity and statistical robustness across multiple validation procedures. All findings are strictly interpreted as empirical regression-level results within the SPARC and LITTLE THINGS datasets. No claims are made regarding new physics, modified gravity, or cosmological universality. External validation on independent surveys remains an open requirement. The Author would like to acknowledge the constructive feedback and methodological insights provided by Mirza Adnan Mohtashim and Yochanan Schimmelpfennig, which contributed significantly to improving the clarity and structural rigor of this work. Their critical perspectives helped refine the analytical framework and strengthen the interpretation of the results.