Einstein–Karahan Framework v123: A Torsion-Based Geometric Approach to Galactic Rotation Curves and the Emergence of a Universal Coherence Scale

We present the Einstein–Karahan Framework v123, a geometrically motivated extension of classical gravitational theory in which spacetime torsion induces an effective dynamical contribution to galactic rotation curves. In contrast to particle-based dark matter models, the framework attributes the observed discrepancies in galactic dynamics to an additional geometric degree of freedom characterized by a dynamically activated torsion field. The model introduces a radial activation mechanism governed by a finite coherence scale, resulting in an effective modification of the rotational velocity profile without altering local gravitational behavior. The resulting phenomenological law is tested against high-quality observational data from the SPARC database using Markov Chain Monte Carlo (MCMC) methods. We perform a multi-galaxy analysis on representative systems (NGC 3198, NGC 2403, NGC 2903, and NGC 891), achieving statistically consistent fits with ²/dof 0. 8 - 1. 2 and physically plausible stellar mass-to-light ratios. Crucially, the torsion coherence parameter rₛ exhibits remarkable stability across galaxies, clustering around rₛ 4. 8, kpc. This emergent scale suggests the presence of a universal geometric structure underlying galactic dynamics. The framework thus transitions from a phenomenological fitting model to a physically motivated effective field theory with predictive capability. While further validation across larger galaxy samples and a full covariant derivation remain necessary, the present results establish the Einstein–Karahan Framework as a promising geometric alternative to dark matter in the description of galactic rotation curves.