The Admissibility Lifecycle: A Complete Structural Framework for System Emergence Stability Control and Collapse

This paper introduces the Admissibility Lifecycle within the Paton System as a complete structural framework describing system existence from emergence through stability control collapse and post-collapse outcomes. Building on prior work the framework integrates admissibility conditions geometric structure system motion intervention and collapse behaviour into a unified lifecycle. Systems evolve within constraint space according to admissibility margin viability gradients curvature and admissible trajectories with control enabling temporary preservation of viability. Collapse occurs when admissibility can no longer be maintained leading to three structurally distinct outcomes: restoration transformation or terminal loss. The framework provides a domain independent account of system behaviour across all phases without modifying underlying governing equations.