The Paton Operator Formalisation: A Structural Definition of Admissible Continuation with Companion Practical Guide

This record contains two connected documents forming a unified release within the Paton System. 1. The Paton Operator Formalisation This paper defines the mathematical structure underlying admissible continuation. It formalises the core operators governing permission, enforcement, production, direction, and condition, and establishes the structural layer beneath system operation. 2. The Paton Operator Formalisation — How to Use It This companion paper translates the formal layer into practical use. It shows how the mathematical operators are applied step-by-step in real systems, enabling evaluation, guidance, and control under constraint. The first paper establishes the formal definition. The second paper provides the practical method of use. Together, they form a complete release connecting mathematical structure with direct application.