Operator Consistency Theorem — Structural Closure of Admissible Operator Systems

This paper formalises the Operator Consistency Theorem within the Paton System. The theorem states that compositions of admissible operators cannot generate internal contradictions provided each operator preserves Boundary, Relation, and Persistence invariants. The result establishes mathematical closure of the operator layer and guarantees stability of composite structural evaluations. The work provides a formal foundation for multi-operator admissibility frameworks across physics, logic, engineering, and complex systems analysis.