Structural Isomorphism as the Fundamental Condition of Commensurability: An Ontological and Epistemological Integration Model Based on YuanXian Theory

This paper, based on the axiomatic system of YuanXian Theory (YXT), proposes and systematically demonstrates the core proposition that “structural isomorphism is the most fundamental condition of commensurability. ” Starting from the four core axioms of YuanXian Theory — True Circle Self-Consistency, Absolute Isolation of the Universe, Self-Referential Mind Field Generation, and Conservation of the Universal Factor — the paper rigorously derives that the underlying geometric structure of the universe is the 64-dimensional toroidal topology (T^64), proving that this structure serves as the common ontological foundation for the physical world, living systems, mathematical order, and conscious phenomena. A “structural hierarchical model of cognitive commensurability” is established by quantifying the “isomorphism degree” (), dividing commensurability into four continuous levels: zero isomorphism, weak isomorphism, strong isomorphism, and full isomorphism. Five representative cases across disciplines are analyzed: • Physical constants (fine-structure constant) as fixed points of the T^64 topology; • The genetic code (64 codons) as a faithful biochemical projection of T^64; • The distribution of Riemann function zeros as a formal translation of the T^64 spectral structure; • Conscious phenomena as the localization of the self-referential mind field; • Religious, artistic, and philosophical symbol systems (e. g. , the 64 hexagrams of the I Ching, mandalas) as diverse cultural compilations of the same underlying structure. The paper concludes that effective cognition and communication are resonance phenomena of the T^64 structure at different scales and modalities. Science, philosophy, art, and religion are unified as different “translations” of the same cosmic ontological structure. Structural isomorphism, rather than identical content, is the deepest condition for commensurability. YuanXian Theory’s T^64 structure and its self-referential dynamics provide the most comprehensive candidate for a “universal structure” to date, offering new foundations and testable predictions for interdisciplinary unification, the hard problem of consciousness, machine understanding, and cosmic cognitive teleology. 本文基於元憲理論 (YuanXian Theory) 的公理化體系, 提出並系統論證「結構同構是通約的最基本條件」這一核心命題。論文從真圓自洽性、宇宙絕對孤立、自指心場生成、宇宙因素守恒四大公理出發, 嚴格推導宇宙底層幾何結構為64維環面拓撲 (T^64), 並證明該結構是物理世界、生命系統、數學秩序與意識現象的共同本體論基礎。 論文建立認知通約性的結構層級模型, 將通約能力分為零同構、弱同構、強同構、全同構四個層級, 並通過物理常數、遺傳密碼、黎曼猜想、意識現象、宗教藝術符號等五個跨領域案例進行驗證。最終指出: 一切有效的認知與交流, 本質上都是T^64結構在不同尺度與模態下的共振。元憲理論為跨學科知識統一、意識難題解決、人工智慧理解問題以及宇宙認知目的論提供了全新的理論基礎與可檢驗預言。