What question did this study set out to answer?

To formalise the Operator Consistency Theorem and validate its implications for operator systems.

February 16, 2026Open Access

Operator Consistency Theorem — Structural Closure of Admissible Operator Systems

Key Points

To formalise the Operator Consistency Theorem and validate its implications for operator systems.
Formalisation of the Operator Consistency Theorem within the Paton System
Analysis of admissible operators preserving Boundary, Relation, and Persistence invariants
Assessment of structural evaluations' stability
Establishment of mathematical closure of the operator layer
Guarantee of stability in composite structural evaluations
Foundation for multi-operator admissibility in various fields like physics and engineering

Abstract

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.

Operator Consistency Theorem — Structural Closure of Admissible Operator Systems

Key Points

Abstract

Cite This Study