The Paton Operator Formalisation: A Structural Definition of Admissible Continuation

This paper defines the mathematical structure underlying admissible continuation within the Paton System. It formalises the core operators governing permission, enforcement, production, direction, and condition, establishing a structural layer beneath system operation. This paper forms a unified release with its companion: “The Paton Operator Formalisation — How to Use It: A Practical Guide to Admissible Continuation,” which provides the applied operational method corresponding to this formal definition.