We propose the Ugentropic Survival Principle, a universal hazard model treating survival as a function of effective options (N_eff, Diversity), Yohaku (μ, breathing room), and structural alignment (δ, inverse of Divergence).The core equation S = N_eff · (μ/μ_c) · e^{-δ} is formally verified in Lean 4 (200+ theorems, 0 unproven).This can be mnemonically expressed as S = N × Y × E (the "S = NYE").The critical threshold μ_c = 1/(2·N_eff) is proposed via mapping from percolation theory. Validated across 8 domains including controlled LLM experiments (3 vendors, 5 models).