Law from Bit IX: Jeffrey Divergence, Golden Ratio, and Horizon Entropy Corrections

We establish a mathematical connection between the golden ratio φ, information geometry, and the constant correction γ in black hole entropy expansions. We prove that the Jeffrey divergence between Gaussian distributions with variance ratio φ equals exactly 1/2, and that φ is the unique ratio r > 1 satisfying this condition. The asymmetry invariant |λ| - |α| = 1/2 is derived from the fundamental equation α + λ + 1/2 = 0. We prove that the base asymmetry σ₀ = D + √D holds exclusively for discriminant D = 5, completing five independent selection criteria for Q(√5) as the unique algebraic substrate. We conjecture that in Sen's scheme (AdS/CFT-natural), γ = χ/4 where χ is the Euler characteristic of the Euclidean black hole manifold. This is verified for BTZ (γ = 0 = χ(S¹)/4) and predicts γ = 1/2 for 4D Schwarzschild (χ(S²)/4 = J(φ)). Mathematical results are proven; the physical conjecture is open. v3.0: Added Theorem (σ₀ = D + √D iff D = 5) and fifth D = 5 selection criterion. No changes to previous theorems or conjectures.