Geometry from Information: Kerr Extension — Weyl Corrections and Anisotropy

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 replaces the Schwarzschild Killing vector as the modular generator, bringing the T_{tφ} component into the Ward identity. Using the correct Kerr Weyl scalar C² = 48(GM)²/Σ³ (Penrose-Rindler), we derive the Weyl correction coefficient: β(M,a,θ) = (GM)²/[60π²Σ²], where Σ = r² + a²cos²θ. This exhibits anisotropy — β depends on polar angle θ, encoding frame-dragging in the information metric. The Schwarzschild result β = (GM)²/60π²r⁴ is recovered at a=0. The Teukolsky equation controls the non-local remainder, extending the OP-1 resolution to the rotating case. Companion paper: DOI 10.5281/zenodo.19029740.