The Tier-3 Admissibility Gate: Structural Permission in the Paton System

The Paton System describes a structural architecture through which systems become distinguishable, interact under constraints, and persist only when admissibility conditions are satisfied. While Tier-2 formation explains how distinguishable structures arise through constrained interaction, systems cannot proceed directly from formation to observation. A structural filtering stage must occur in which only configurations capable of persistence are permitted to continue. This paper formally defines Tier-3 of the Paton System as the Admissibility Gate: the structural layer that determines whether a formed configuration is permitted to persist and enter the observation domain. The admissibility gate is characterised through the Boundary–Relation–Persistence (BRP) condition and operationalised through the Paton Admissibility Test (PAT) and the Unified Admissibility Equation. The result is a minimal structural mechanism explaining why only a subset of possible configurations becomes observable systems.