The Peak Ruin Law

This paper unifies domain-specific threshold failure mechanisms—structural engineering (ultimate load theory), finance (margin requirements), toxicology (lethal dose limits), and stochastic processes (first-passage times)—into a single cross-domain framework. I introduce the Peak Ruin Law: systems with absorbing failure states (where recovery cannot preserve identity) collapse if and only if peak stress exceeds a critical threshold, independent of cumulative performance. Monte Carlo simulation with 10,000 stochastic paths demonstrates: Survival probability collapses sharply at V{crit} (ρ = –0.94), regardless of average performance. Cumulative returns show near-zero correlation with survival (ρ = 0.03). Time-to-ruin concentrates at first-passage events. Survival operates hierarchically above optimization. Extension to time-varying thresholds shows systems fail under constant stress when degradation reduces V{crit} below experienced levels. This work establishes peak-based survival as a distinct system law, mathematically independent from and hierarchically prerequisite to optimization principles.