Defining AI Agents: An Ontological and Topological Framework for Organizational Systems

The scalability and governance challenges of AI agents trace back to a fundamental architectural deficit: the absence of an explicit, semantically expressive, and structurally adaptive abstraction layer. This paper introduces an architectural framework utilizing explicit, machine-readable ontological and topological representations for AI agents. Leveraging category theory, mereotopology, and graph theory, it formally defines the framework and proves five core properties: composability, interoperability, provenance preservation, auditability, and formal verifiability.