Electromagnetic Kantowski–Sachs Solutions in Teleparallel F(T) Gravity

We construct electromagnetic Kantowski–Sachs (KS) solutions in covariant teleparallel F(T) gravity using the coframe/spin–connection (CSC) formalism. In the restricted branch considered here, the Maxwell conservation laws (CLs) impose strong restrictions on the anisotropic scale factors and lead to the scaling ρ_{em} A_3^{−4}. We derive the corresponding symmetric and antisymmetric field equations (SFEs and AFEs) and formulate a reconstruction scheme in which F(T) is determined from the KS dynamics rather than imposed a priori. Power-law (PL) and exponential (EXP) coframe ansätze generate distinct invariant reconstruction branches, including scaling cosmologies, teleparallel de Sitter (TdS) regimes, and KS black-hole-interior-like reconstruction branches. The resulting models are organized using the Coley–Landry invariant classification and analyzed through leading-order stability conditions F_T>0 and F_{TT}>0.