The Paton System — Structural Connection Map

This document presents a structural connection map of the Paton System, defining the relationship between its canonical equations, operational methods, structural laws, geometric representations, lifecycle dynamics, and cross-domain applications. Unlike architectural or status representations, this map explicitly organises how individual papers within the Paton System interrelate as a unified research framework. The canonical equations (I–X) act as the reference spine, from which operational, structural, geometric, and domain-specific works extend in a layered structure. The document clarifies the internal coherence of the system by distinguishing between: Canonical definition (equations) Operational application (methods and operators) Structural laws (persistence and collapse conditions) Geometric representation (admissible regions and boundary structure) Lifecycle progression (recursive system evolution) Cross-domain instantiation (applications across physics, AI, biology, cognition, and organisational systems) This mapping establishes the Paton System as a non-fragmented, structurally integrated framework, demonstrating how distributed publications form a single coherent architecture governed by admissibility and constraint compatibility.