The Karahan Framework v71.0: A Minimal Nonlinear Teleparallel Gravity Model Linking Precision Cosmology, Regular Compact Objects, and Torsion-Induced Shadow Observables

We present the Karahan Framework v71.0 as a minimal and analytically tractable extension of teleparallel gravity based on the nonlinear model �. The construction follows a strict minimality principle, introducing a single additional parameter while preserving the General Relativity limit.On cosmological scales, the model yields a closed modified Friedmann system with an exact solution for the normalized expansion function �, ensuring consistency with �CDM at late times while allowing controlled deviations at high energy densities. Observational constraints restrict the torsion parameter to small values, confirming compatibility with current data.In the strong-gravity regime, a phenomenological metric replaces central singularities with regular cores, maintaining Schwarzschild behavior at large radii. This provides a mathematically consistent pathway toward non-singular compact objects.A novel observational sector is introduced through torsion-induced shadow deformation. The black hole shadow is parameterized by an anisotropic boundary function, enabling a direct link between torsion effects and observable deviations from circularity. A minimal likelihood framework combines shadow size and non-circularity, allowing the first numerical constraints on the deformation parameter.The framework is not presented as a complete theory of gravity but as a minimal, consistent, and testable model. Its key result is that nonlinear torsion corrections can be introduced in a controlled manner, remain compatible with precision cosmology, and generate observable signatures in strong gravitational regimes.