The Paton Operator Set A Minimal Operational Framework for Admissible Continuation

This paper defines a minimal operational framework for admissible continuation within the Paton System. It formalises a set of core operators that determine whether system states may persist under constraint. Admissibility is established as the governing condition of continuation, enforced through the Paton Admissibility Test (PAT) at each transition. Recursive propagation is permitted only when states remain constraint-compatible, producing a structurally gated system in which continuation is conditional rather than unrestricted. The operator set provides a domain-neutral method for evaluating system stability, filtering trajectories, and maintaining persistence under constraint. The framework does not introduce new domain-specific laws but operates as a pre-theoretical layer determining whether continuation is permitted before domain dynamics apply.