Karahan Framework v121: A Nonlinear Torsion-Based Effective Field Theory for Galactic Dynamics Without Dark Matter

Karahan Framework v121: A Nonlinear Torsion-Based Effective Field Theory for Galactic Dynamics Without Dark Matter We present the Karahan Framework v121, a nonlinear torsion-based effective field theory (EFT) that aims to explain galactic rotation curves without invoking dark matter. The model is constructed from the torsion sector of spacetime and introduces a coarse-grained scalar invariant T₄₅₅ derived from the torsion tensor. Unlike linear formulations that lead to Yukawa-type decay, the present framework promotes the effective dynamics to a nonlinear regime, allowing the large-scale field profile to deviate from exponential falloff. We show that, under a well-defined asymptotic halo condition dT₄₅₅/dr 1/r, the effective torsion field approaches a logarithmic radial dependence, naturally supporting approximately flat galaxy rotation curves. The resulting modification to the circular velocity law arises as a gradient force term added to the standard baryonic contribution, preserving consistency with geodesic motion on a Levi-Civita background. The framework further incorporates an emergent scaling relation T₄₅₅ M, which, combined with a saturation of the torsion coherence length in the outer halo, leads to consistency with the baryonic Tully–Fisher relation v⁴ M. Subleading oscillatory corrections are interpreted as interference effects within a distributed network of compact rotating sources and do not affect the dominant halo behavior. The Karahan Framework v121 provides a geometrically motivated, nonlinear alternative to particle dark matter and establishes a testable connection between compact-object physics and large-scale galactic dynamics.