Synthesis, Generation, Circulation:Three Parallel Ontological Routes — Isomorphic Legitimacy and Research Programmes of the Convergent, Generative‑Life, and Cyclic Paradigms

Drawing upon the SubstanceFunctionTelos metaaxiom set, this paper constructs the ontologyaxiomset space and demonstrates three minimallycomplete, mutuallyirreducible ontological routes aligned with Synthesis, Generation and Circulation: the convergentorientation convergent paradigm (Synthesis: All Stable Structures are Mathematizable, The World Prefers Parsimony, Topological Unification), the unfoldingorientation generativelife paradigm (Generation), and the cycleorientation cyclic paradigm (Circulation). Rather than a dispute over truthversusfalsehood, the three routes represent distinct ontological truncations applied to one shared substrate, each possessing selfconsistent questioning prerogatives, criterion systems and compatible research domains. This paper completes SubstanceFunctionTelos instantiation and internal selfconsistency verification for the three axiomsets, and presents an operational threequestion criterion for paradigm attribution. Engaging with the philosophyofscience corpus of Kuhn, Popper and Feyerabend, it argues that their analyses remain confined to superficial descriptions of paradigms and fail to reach the root source: metalayer axiomselection. Further, it conducts isomorphic crossreading of Confucian, Buddhist and Daoist intellectual traditions, showing that the open system articulated by SynthesisGenerationCirculation can accommodate subjectivity, contradiction transformation and spiral evolution. The paper demarcates boundaries, crossinterface rules and incommensurability conditions for the three paradigms, formulates associated research programmes and observable clues for each route, and opens legitimate research avenues beyond the convergent paradigm for the study of life, consciousness, civilisational history, ecology, Chinesemedicine qitransformation, and AGI. It also delivers an operational threequestion paradigmattribution criterion — whether substance is divisible; whether function is static or dynamic; whether telos converges, generatesunfolds, or cycles — enabling rapid identification of the ontologicaltruncation orientation for any given study, theory or AGI route and preventing paradigmmismatch.