Admissible Flow and Resolution: A Structural Account of the Tier 0 → Tier 1 → Tier 2 → Tier 3 → Tier 4 Transition

This paper presents a structural account of how reality emerges through constraint filtering within the Paton System. It formalises admissibility as the governing condition that determines which configurations may persist from undivided availability (Tier 0) through distinction (Tier 1), possibility (Tier 2), and constraint filtering (Tier 3), into realised structure (Tier 4). At the level of formation, multiple candidate trajectories coexist. As these trajectories approach the admissibility boundary, constraint intensifies, eliminating incompatible paths while compressing viable trajectories into a bounded admissible corridor. Only configurations that remain internally consistent under constraint are permitted to continue. The resulting structure is not selected or optimised, but emerges as the only configuration that survives without contradiction. From the human perspective, this process is experienced as smooth, continuous flow, often interpreted as a path of least resistance. Structurally, however, this corresponds to continuation within an admissible corridor. The paper establishes a unified formation-to-resolution pipeline, demonstrating that distinction enables possibility, possibility generates trajectories, and admissibility determines continuation. This provides a minimal structural mechanism for the transition from availability to reality without invoking selection, optimisation, or additional physical laws.