The Karahan Framework v78.0: Minimal Torsion Cosmology with Vortex-Induced Accretion and Black Hole Shadow Signatures

We present the Karahan Framework v78.0, a minimal nonlinear extension of teleparallel gravity defined by the function �. The model preserves the General Relativity limit while introducing a single additional parameter controlling nonlinear torsion effects.At the cosmological level, the framework provides an exact analytical solution for the normalized expansion function �, ensuring full mathematical control and a well-defined physical domain. Observational constraints from late-time expansion data restrict the torsion parameter to small values, maintaining consistency with the �CDM model.In the strong-gravity regime, the framework introduces a regularized compact-object structure together with an axisymmetric torsion-vortex extension. This vortex-like geometry modifies the surrounding spacetime and leads to anisotropic deformations of black hole shadows.In addition, the model naturally predicts a modified accretion behavior. The torsion-induced vortex structure acts as an effective angular momentum transport mechanism, leading to spiral inflow patterns and localized density enhancements in the accretion flow. This provides a direct physical interpretation of how torsion effects can influence observable emission structures near the event horizon.A minimal coupling between cosmological torsion and observable shadow deformation is introduced via a linear relation between the torsion parameter and the deformation amplitude. The combined framework connects cosmology, compact objects, and observational signatures within a unified and testable structure.The Karahan Framework is not intended as a complete theory of gravity, but as a minimal, mathematically consistent, and observationally testable model. It demonstrates that nonlinear torsion effects can remain hidden in the late universe while becoming relevant in extreme gravitational environments, offering a clear pathway toward detecting new gravitational physics.