The Paton System — Unified Generative–Admissibility Architecture (PS-UNI v1.0)

Abstract: This paper formalises the unified structural foundation of the Paton System as a three-stage architecture consisting of recursive generation (℘), Tier-indexed admissibility (Tier-3), and multi-scale temporal continuity (Tier-8). Structured continuation is defined as the sustained admissibility of recursively generated candidates under Tier-indexed datum contracts. The datum is formally defined as a reference constraint contract Dₖ = (Xₖ, Cₖ), specifying the admissible region within a representation domain. Admissibility is binary. Continuation requires cross-tier and temporal persistence across required tiers and time indices. The architecture consists of: Recursive candidate generation (℘). Tier-indexed admissibility evaluation under datum contracts. Cross-tier and temporal continuity requirements. All previously defined Paton System constructs — including Paton Assist (ΠPA), Paton Compass, the BRP admissibility function, Structural Honesty Gate, Mass–Size Gate, Resolution Ceiling Operator (RCO), and the Tier 0–8 framework — are formally shown to instantiate this unified generative–admissibility–continuity structure. The framework introduces no new physical laws, supersedes no governing mathematics, and asserts no ontological substrate. It operates strictly within classical logic as a structural admissibility formalism. Removal of any core component — generation, datum contract, admissibility gate, or continuity requirement — collapses system coherence, establishing structural necessity. PS-UNI v1. 0 serves as the canonical unification layer for the Paton System. Future domain-specific publications instantiate this architecture without modifying its foundational structure.