Abstract

This work presents the Admissibility Lifecycle within the Paton System as a structural diagram describing system existence from emergence through stability motion control collapse and post-collapse outcomes. Systems enter admissible space through admissibility and reachability conditions and evolve according to admissibility margin viability gradients curvature and admissible trajectories. Control mechanisms act to preserve admissibility until structural thresholds are reached. Collapse occurs when admissibility can no longer be maintained leading to post-collapse dynamics and three distinct outcomes: system re-entry successor formation or terminal collapse. This diagram provides a domain independent visual representation of the full system lifecycle without modifying underlying governing equations.