Terminal Collapse: A Structural Criterion for Non-Recoverable System Loss

This paper introduces Terminal Collapse within the Paton System as a structural criterion for non-recoverable system loss. Building on Post-Collapse Dynamics and System Re-Entry the framework defines terminal collapse as the condition in which no admissible restoration of the original system is possible and no structurally related admissible successor can be formed from any reachable post-collapse configuration. The paper distinguishes terminal collapse from recoverable collapse transformational collapse and temporary inadmissibility. It establishes terminal collapse as a structural property arising from constraint violation loss of admissible trajectories and breakdown of structural continuity. This provides a domain independent method for identifying final system loss without modifying underlying governing equations.