Sandhi: A Failure-Transition Diagnostic Framework Demonstrated via AI Training Dynamics

This paper formalizes Sandhi as a universal failure-transition diagnostic framework for complex systems. Sandhi is defined as an irreversible intermediate state in which system outputs remain continuous while the assumptions underlying governing equations silently fail. Using AI training dynamics as a worked demonstration, the paper completes a full diagnostic cycle by: Detecting Sandhi through a loss-based transition criterion, Classifying Sandhi by the performance dimension that degrades, and Explaining why existing optimization equations are structurally blind to such transitions. Rather than proposing a new optimization method, this work establishes Sandhi as a diagnostic science that explains why failures occur even when equations remain locally valid. The framework is intentionally domain-independent, allowing other fields to derive application-specific detection terms without rederiving the core theory. This paper serves as a keystone formalization linking prior Sandhi applications and enabling systematic failure analysis across AI, physics, materials, medicine, and engineering systems.