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

omplex systems. When constraints governing system behavior become correlated, efec-tive diversity collapses toward unity formalized as kef = k/(1 + ρ(k − 1)) → 1 as ρ → 1.The kef formula derives from the Kish design efect, providing a mathematically groundedmeasure of eective degrees of freedom.We derive three collapse timelines (Ttruth, Tentropy, Tcapture) with closed-form expressionsand identify a singularity boundary (Kreq · ρ ≥ 1). The framework provides phase classi-fication (chaos/healthy/rigidity) and documents domain-specifc temporal patterns acrossfnancial, institutional, and electrochemical systems. Verifed through Monte Carlo simula-tion and Lean 4 proofs.Temporal precedence patterns are domain-specifc: ρ rises before financial crises(+0.14) and institutional transitions (+0.17), but falls before battery failure (−0.25). Theframework measures; domain experts interpret.