Einstein–Karahan Framework v125: A Mass-Dependent Torsional Scaling Law for Galactic Rotation Curves

We present version v125 of the Einstein–Karahan Framework, a torsion-based approach to modeling galactic rotation curves without invoking dark matter. In contrast to earlier versions, where the torsional activation scale r_s was treated as a free parameter, we introduce a global scaling relation that links r_s directly to observable galaxy properties. Using a global fit across a sample of galaxies, we find that the activation scale follows a mass-dependent relation of the form: r_s proportional to M_bar^0.3 This result indicates that the torsional coherence length is not a universal constant, but instead emerges from the baryonic mass distribution. The geometric dependence is found to be negligible within the current analysis. The framework thereby transitions from an empirical curve-fitting model to a predictive physical description with intrinsic structure. While the present results are based on a reduced dataset and discrete parameter sampling, they demonstrate the viability of a mass-driven torsional mechanism in galactic dynamics. Further validation using the full SPARC dataset and continuous statistical methods is required. Nevertheless, the identified scaling relation represents a key step toward a falsifiable and physically interpretable alternative to standard dark matter models.