Admissibility Lifecycle: Structural Diagram of System Emergence Stability Control and Collapse

This work presents the Admissibility Lifecycle as a single-page structural diagram within the Paton System. The diagram summarises the complete system lifecycle from emergence through stability motion basin structure control threshold collapse and post-collapse outcomes. Systems are shown to enter admissible space through admissibility and reachability conditions evolve according to admissibility margin gradient and curvature move along admissible trajectories and transition between stability basins. Control mechanisms act to preserve admissibility until structural thresholds are reached. Collapse occurs when admissibility margin is no longer maintainable leading to post-collapse dynamics and three distinct outcomes: system re-entry successor formation or terminal collapse. This diagram provides a visual reference for the full lifecycle framework without modifying underlying governing equations.