Admissible Flow and Resolution A Structural Account of the Tier 2 → Tier 3 → Tier 4 Transition

This paper defines admissibility as the structural condition governing the transition from possible configurations to realised structure through constraint filtering. Within the Paton System, systems do not select or optimise trajectories. Instead, multiple candidate transitions emerge at the level of formation (Tier 2), and only those that remain internally consistent under constraint can continue. As trajectories approach the admissibility boundary (Tier 3), incompatible paths collapse while viable trajectories compress into a bounded admissible corridor. Only these constraint-consistent trajectories pass through the admissibility gate. The resulting structure at Tier 4 is not selected or optimised, but emerges as the only configuration that survives constraint without contradiction. From the human perspective, this process is experienced as smooth, continuous flow, often described as a path of least resistance. Structurally, this corresponds to continuation within an admissible corridor, where constraint violation is minimised and coherence is preserved. This paper formalises admissible flow as the minimal mechanism governing transition from possibility to observable structure, establishing constraint compatibility as the determinant of system continuation across all domains.