Coherence Collapse Analysis: A Universal Failure Mode in Complex Coordinating Systems

 Coherence Collapse Analysis (CCA) is an engineering risk framework for identifying correlation-driven failure modes in complex systems. When constraints governing system behavior become correlated, effective diversity collapses toward unity, formalized as k_eff = k/(1+ρ(k-1)) → 1 as ρ → 1. The k_eff formula derives from the Kish design effect, providing a mathematically grounded measure of effective degrees of freedom.

  We derive three collapse timelines (T_truth, T_entropy, T_capture) with closed-form expressions and identify a singularity boundary (K_req · ρ ≥ 1). The framework provides phase classification (chaos/healthy/rigidity) and documents domain-specific temporal patterns across financial, institutional, and electrochemical systems. Verified through Monte Carlo simulation and Lean 4 proofs.

  Key finding: Temporal precedence patterns are domain-specific: ρ rises before financial crises (+0.14) and institutional transitions (+0.17), but falls before battery failure (−0.25). The framework measures; domain experts interpret.

  Limitation (L-01): ~40% of emergent deception patterns are fundamentally undetectable by methods operating on marginal distributions. CCA provides partial detection (~60% coverage), not complete safety guarantees.