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

This paper defines the Paton Operator Calculus, a structural framework governing how operators combine into admissible execution paths within the Paton System. Building on the Paton Operator Formalisation and Operator Set, this work establishes the rules of operator composition, sequencing, and chain validity under admissibility constraint. It formalises how systems execute step by step while preserving structural permission to continue. The framework introduces no new domain-specific laws and does not modify governing equations. It operates as a pre-theoretical layer determining when operator sequences remain admissible and when continuation must terminate. This paper is 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 Together, these define how systems execute, degrade, and select paths under constraint. CONCEPT DOI (use this public link) https://doi.org/10.5281/zenodo.19594967