We present the Karahan Framework, a minimal nonlinear extension of teleparallel gravity defined by �, which introduces a dynamical torsion sector while preserving the empirical success of the standard �CDM cosmology in the limit �. The resulting modified Friedmann equation, �, admits an analytic solution and remains fully consistent with observational constraints at late times.A comprehensive 100000-sample Occam analysis demonstrates that the torsion parameter � is tightly constrained around zero in the cosmological background, ensuring compatibility with current data while leaving open the possibility of detectable deviations in strong-gravity regimes.To extend the framework, we introduce a spin-dependent energy partition mechanism that replaces the fixed 95/5 assumption with a dynamical law �, describing the fraction of energy converted into visible matter at the outer ring structure of a rotating system. In this picture, the total energy flow decomposes into an axial bypass component and a matter-forming boundary component, with the present-day matter fraction emerging as a specific value � at a characteristic spin state.The framework predicts that torsion effects remain effectively hidden in the cosmological background but can become observable in extreme gravitational environments, particularly through deviations in black hole shadow geometries characterized by �. This establishes black hole imaging as a primary observational channel for testing torsion-driven physics.
Asil Karahan (Sat,) studied this question.