Toward a Dynamical Theory of AI Failure: Phase Transitions, Relaxation Time, and Distinct Cognitive

This work introduces a dynamical framework for analyzing AI system behavior under constraint. We show that AI systems do not exhibit a universal recovery structure, but instead fall into distinct dynamical regimes characterized by continuous versus discrete recovery behaviors. Through controlled experiments, we identify:(1) phase transition points under constraint strength,(2) relaxation time distributions, and(3) distinct failure modes including internal collapse and boundary-driven persistence. This work extends the Puzzle Structural Theory (PST) research line.