The Paton Operator Calculus: Composition, Sequencing, and Admissible Execution Paths

This paper defines the Paton Operator Calculus, a structural framework governing the composition and sequencing of operators under admissibility constraint. Building on the Paton Operator Formalisation and Operator Set, this work establishes how operators combine, how execution paths are formed, and how validity is preserved across sequential transitions. The framework introduces no new domain-specific dynamics and does not modify governing equations. Instead, it provides a pre-theoretical structure determining when operator chains remain admissible and when continuation must terminate. The result is a general, domain-neutral method for constructing admissible execution paths across complex systems. This paper forms part of the Paton Operator Layer and is structurally linked with: Operator Stability and Failure: Admissibility Breakdown Under Sequential Constraint Admissible Operator Optimisation: Selection and Efficiency Within Constraint Boundaries DOI zenodo.19604966