Admissible Operator Optimisation: Selection and Efficiency Within Constraint Boundaries

This paper defines admissible operator optimisation within the Paton System, establishing how execution paths are selected and evaluated under constraint. Building on the Paton Operator Calculus and Operator Stability frameworks, this work formalises how systems choose among multiple admissible paths while preserving viability. It introduces efficiency as a constrained measure, where optimisation is permitted only within admissible regions and must not compromise continuation. The framework introduces no new domain-specific laws and does not modify governing equations. It operates as a pre-theoretical layer determining how admissible paths are ranked, selected, and maintained under constraint. This paper is part of the Paton Operator Layer and is structurally linked with: - The Paton Operator Calculus: Composition, Sequencing, and Admissible Execution Paths - Operator Stability and Failure: Admissibility Breakdown Under Sequential Constraint Together, these define how systems construct, degrade, and select execution paths under constraint. CONCEPT DOI (use this public link) https://doi.org/10.5281/zenodo.19594967