Operatorization: A Framework for Transforming Fixed Solutions into Executable Knowledge

Abstract Human knowledge has traditionally been preserved as static artifacts, including theorems, algorithms, logical principles, formal proofs, and procedural descriptions. Although these representations have enabled scientific and technological progress, they remain primarily interpretable rather than directly executable by intelligent systems. This paper introduces Operatorization, a computational framework for transforming fixed solutions into executable knowledge. Instead of representing knowledge solely as static objects, the framework extracts reusable behavioral structures, constraints, invariants, and operational semantics, enabling their conversion into machine-executable operators. The paper presents the conceptual foundations of Operatorization, a formal operator representation model, implementation architecture, evaluation framework, benchmark experiments, and potential applications to explainable artificial intelligence, computational reasoning, knowledge engineering, and reusable AI systems. Keywords: Operatorization, Executable Knowledge, Knowledge Representation, Explainable Artificial Intelligence, Computational Reasoning.