Geometry from Information: Kerr Extension — Anisotropic Weyl Corrections, Frame-Dragging, and Teukolsky Resolution

We extend the Geometry from Information (GFI) programme to the Kerr rotating black hole. The key observation is that the Kerr horizon null generator ξ = ∂_t + Ω_H ∂_φ serves as the modular generator, bringing T_{tφ} into the Ward identity. Using the Penrose-Rindler Weyl scalar C² = 48(GM)²/Σ³, we derive: β(M,a,θ) = (GM)²/[60π²Σ²], where Σ = r² + a²cos²θ. This exhibits anisotropy encoding frame-dragging in the information metric. The non-local remainder is resolved via the Teukolsky equation, which is the Newman-Janis complexification of the Regge-Wheeler equation (r → r - ia·cosθ). OP-1 is resolved for the rotating case: V_Teuk vanishes at the horizon (Δ=0) and is subleading at large r. Companion paper (Schwarzschild): DOI 10.5281/zenodo.19029740.