Structure-Triggered Geometric Response in Galaxies: A Compactness-Driven Alternative to Dark Matter with Predictive η Activation

We present a structure-dependent softening model for galactic rotation curves, derived directly from baryonic observables. Instead of treating deviations from standard models as stochastic or purely mass-dependent, we introduce a predictive softening term (η_soft) that is inferred from internal galaxy structure, including gas distribution, disk morphology, and compactness. Using a sample of 143 galaxies from the SPARC dataset, the activation of the softening term is predicted with high accuracy (ROC-AUC ≈ 0.92), indicating a strong and systematic dependence on baryonic structure. The resulting model improves fits over standard NFW halo models in 105 out of 143 galaxies, with a median ΔBIC(soft − NFW) ≈ −60.65. These findings suggest that the effective gravitational response in galaxies depends not only on total mass, but also on the internal distribution and state of baryonic matter. The proposed model provides a reproducible, data-driven extension to standard galactic dynamics frameworks. While the softening term is currently phenomenological, it offers a well-defined empirical target for future theoretical work on structure-dependent modifications of gravity.