Failure as Constraint Incompatibility: A Unified Structural Account Across Systems

Failure is typically interpreted as a breakdown in behaviour, prediction, or control within domain-specific systems. This paper presents a structural reinterpretation: failure occurs when system constraints can no longer be jointly satisfied, eliminating all admissible continuation paths. Within the Paton System, failure is not an event but a boundary condition. A system persists only while its governing constraints remain mutually compatible. When no configuration exists that satisfies all constraints simultaneously, continuation is no longer possible. Failure is therefore defined as the loss of admissible continuation under constraint. This work unifies prior Paton System contributions on admissibility failure, collapse thresholds, constraint compatibility, and boundary detection into a single minimal formulation. Selected examples from biological, governance, and computational systems are provided, while broader applicability across multiple domains is acknowledged. The paper does not introduce new domain-specific dynamics. It provides a pre-theoretical structural condition governing when systems are permitted to continue.