Galaxy Rotation Curves Show a Surface-Density–Dependent Transition Geometry (κ–Σ) That MOND Does Not Reproduce: A Surface-Density-Constrained, Non-Tuned Framework Evaluated on 174 SPARC Galaxies

Abstract We present a recursive regime model for galaxy rotation curves in which the effective saturation parameters (Ω, λ) are not freely tuned per galaxy, but instead approximated from observable baryonic structure. Specifically, Ω and λ are expressed as simple log-linear functions of a baryonic surface-density proxy Σ ≈ M_b / r_d² derived directly from SPARC rotation curve data. The model incorporates a recursive contribution to velocity, modulated by a radius-dependent damping term exp(−r/r_d), which prevents outer-radius divergence and stabilizes high-mass systems. Across a sample of 174 SPARC galaxies, the model achieves an average RMSE of 26.1 km/s in-sample and 26.8 km/s under leave-one-out validation, approaching the performance of standard MOND (24.5 km/s) while requiring no per-galaxy parameter fitting. These results demonstrate that the model operates within a shared structural regime that is strongly constrained by measurable baryonic distribution, generalizes robustly to unseen systems, and does not depend on fine-tuned parameters.