The Tier-2 → Tier-3 Transition: From Formation to Admissibility in the Paton System

The Paton System describes a structural architecture through which distinguishable systems emerge, interact under constraints, and persist only when admissibility conditions are satisfied. While Tier-2 explains the formation of distinguishable configurations through constrained interaction, not all formed configurations are capable of persistence. A structural transition must therefore occur between formation and admissibility. This paper defines the Tier-2 → Tier-3 transition as the phase in which candidate structures emerging from constrained flow are evaluated for structural viability. The transition marks the movement from formation dynamics to the admissibility gate defined by the Boundary–Relation–Persistence framework. Within the Paton System architecture, Tier-2 generates a space of possible configurations through constrained interaction. Tier-3 acts as the structural gate determining which of those configurations satisfy the conditions required for persistence. The transition between these layers therefore functions as a filtering stage separating transient formation from viable structural continuation. By clarifying the Tier-2 → Tier-3 transition, this paper completes the minimal pathway through which systems move from formation to admissibility and ultimately become eligible for observation within the Tier-4 datum interface. The transition helps explain why only a small subset of formed configurations persist across domains ranging from physics and biology to optimisation and control theory.