The Paton Operator Layer: A Unified Framework for Admissible Execution

This paper presents the Paton Operator Layer as a unified framework for admissible execution within the Paton System. It consolidates five components: the Operator Formalisation, Operator Set, Operator Calculus, Operator Stability and Failure, and Admissible Operator Optimisation. Together, these define how systems evaluate, construct, maintain, and select admissible execution paths under constraint. The framework introduces no new domain-specific laws and does not modify governing equations. It operates as a pre-theoretical execution architecture determining when continuation is permitted, how it proceeds, when it becomes unstable, and how viable paths are selected. This paper serves as an integrative map linking the operator layer components: - The Paton Operator Formalisation: A Structural Definition of Admissible Continuation - The Paton Operator Set: A Minimal Operational Framework for Admissible Continuation - The Paton Operator Calculus: Composition, Sequencing, and Admissible Execution Paths - Operator Stability and Failure: Admissibility Breakdown Under Sequential Constraint - Admissible Operator Optimisation: Selection and Efficiency Within Constraint Boundaries Together, these establish a complete execution architecture within the Paton System. CONCEPT DOI (use this public link) https://doi.org/10.5281/zenodo.19594967