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

We present the Karahan Framework v121, a nonlinear torsion-based effective field theory (EFT) that aims to explain galactic rotation curves and strong-gravity observables without invoking particle dark matter. The framework originates from the torsion sector of spacetime geometry and introduces a coarse-grained scalar invariant T₄₅₅ as the macroscopic degree of freedom relevant for astrophysical scales. In contrast to linear formulations that yield Yukawa-type decay, the effective dynamics are promoted to a nonlinear regime, allowing the large-scale torsion field to develop a logarithmic asymptotic profile. By imposing the halo closure condition dT₄₅₅/dr 1/r, the model naturally supports approximately flat galactic rotation curves. Matter trajectories are described on an effective Levi-Civita background, while torsion contributes as an explicit gradient force term, ensuring consistency with standard geodesic motion at leading order. The framework further achieves structural consistency with the baryonic Tully–Fisher relation through a combination of emergent scaling T₄₅₅ M and saturation of the torsion coherence length in the outer halo, leading to an effectively constant coupling parameter. Subleading oscillatory corrections are interpreted as collective interference effects within a distributed network of compact rotating sources and do not affect the dominant halo dynamics. In the strong-gravity regime, the framework predicts a small but non-zero black-hole shadow non-circularity in the approximate range ₒ₇ 0. 01–0. 03, providing a falsifiable target for next-generation horizon-scale observations such as the ngEHT. The Karahan Framework v121 thus offers a geometrically motivated, nonlinear alternative to dark matter with explicit observational predictions spanning both galactic and horizon-scale phenomena.