The Quantized Action Cavity Postulate: Derivation of α⁻¹, Closure Law, Gravity and Black Hole Information

The Quantized Action Cavity Postulate: We postulate R≡ħ, ε_min≡e²/c, α≡ε_min/R. Optimal fraction 1/Φ²=0.381966, θ_ideal=360/Φ²=137.507°. We prove Closure Law: Nθ≡0 mod 360 for d|360 with digital root 9≡0 (3°,6°,9°,18°,36° fail). Golden angle root 5 is only non-closing (Hurwitz). Isotropic pressure ∇P_info=0 → S¹ membrane, stress concentration K_t. Periodic angles give K_t→∞ → collapse S¹→{0}. Golden gives K_t=1 → uniform tension γ → constant G with |Ġ/G|<1e-13, and G_eff=G·K_t→∞ at closure defect (black hole). Information preserved on membrane → S_BH~A/4Lp², recovering Hawking area law confirmed by GW250114 (PRL 135,111403, 2025). Quantum smearing b1=Φ²/√π=1.477149 gives α⁻¹=137.036 at two-loop with zero free parameters. Predictions: α⁻¹(Mz)=127.92, ρ_Λ~1e-122, Δα/α=2.1e-18/km, no G variation in voids.