Axiom Set of Cognitive Ontology:All Stable Structures are Mathematizable, The World Prefers Parsimony, Topological Unification

This paper presents a minimally complete ontology axiom set structured under the tripartite template of substancefunctiontelos: All Stable Structures are Mathematizable, The World Prefers Parsimony, Topological Unification. This axiom set addresses the core ontological question: why and in what form the world can be cognized. The paper systematically elaborates the construction template, construction difficulties, verification criteria and intrinsic isomorphic relations of the axiom set. It clarifies the hierarchical boundary between ontological axioms and metacognitive axioms, and demonstrates that as the underlying world model of a cognitive operating system, this axiom set can support ontological folding operations, convergent AGI and scientific modelling paradigms. Meanwhile, at the top structural level, it establishes an equal communication pathway for Eastern and Western intellectual paradigms, rather than simple patchwork, by tracing back to the structural substrate of being itself. This paper also specifies that this ontology axiom set is not the only picture of reality; it is merely one ontological substrate. It opens up a space of complete ontology axiom sets for cognitive systems of different orientations to mount autonomously.