The Karahan Framework v41.2 CLEAN: Precision Cosmology in Minimal Nonlinear Teleparallel Gravity

We present the Karahan Framework v47.0 as a minimal extension of teleparallel gravity based on the nonlinear model F(T) = T + ξT². The construction follows the principle of minimality, introducing a single additional parameter while preserving the General Relativity limit. At the cosmological level, the model yields a closed modified Friedmann equation with an exact analytical solution for the normalized expansion function E(z). A multi-fluid extension ensures consistency with late-time cosmology and enables direct comparison with observational data. Fits to H(z) measurements constrain the nonlinear torsion parameter α to remain small, indicating agreement with ΛCDM at low redshift. In the strong-gravity regime, a minimal phenomenological ansatz replaces central singularities with regular cores while recovering standard Schwarzschild behavior at large scales. The framework is not proposed as a complete theory of gravity, but as a mathematically consistent and observationally testable minimal model. Its main result is that nonlinear torsion corrections can be introduced in a controlled way, remain compatible with precision cosmology, and provide a pathway toward non-singular gravitational structures.