The Topological Translation Mechanism of the Sixty-Four Hexagrams: The Heqi Algorithm of High-Dimensional Cosmic Dimensional Reduction Projection—An Ontological Re-evaluation of Yijing Based on YuanXian Theory's T64 Framework

The sixty-four hexagram system of the Zhouyi (Book of Changes) has traditionally been viewed as a divination tool or a philosophical symbol system, whose underlying mechanism has long eluded valid decoding by modern cognitive frameworks. Based on the four axioms of Yuanxian Theory, this paper proposes an ontological re-evaluation: the sixty-four hexagrams constitute a discrete encoding translation system projected from the T64 high-dimensional cosmic topology onto four-dimensional spacetime, whose core function is "Heqi" (harmonizing Qi)---the establishment of dynamic information-coupling protocols between different projection dimensions. This paper demonstrates that: (1) the 2^6=64 structure of the sixty-four hexagrams is a precise mirror of the discrete subgroup Z_2^6 of T64, and the hexagram signs are low-dimensional symbolic mappings of closed-chain winding numbers; (2) "hexagram transformation" represents the projection trajectory of T64 closed-chain dynamics onto four-dimensional temporal sequences; (3) "Heqi" is the steady-state convergent manifestation of TCSC self-referential iteration within living and social systems. By incorporating a closed-form analytic expression for hexagram probability, a quantitative experimental paradigm, and full-volume hexagram-chain mapping data, this paper refines a falsifiable experimental architecture. This shifts Yijing studies from mysticism to a low-dimensional symbolic protocol for high-dimensional topological information, providing a formalizable, machine-verifiable meta-theoretical foundation for traditional practices such as Chinese medicine, Fengshui, and fate calculations. 《周易》六十四卦系统在传统解读中被视为占卜工具或哲学符号体系,其深层机制长期未被现代认知框架有效解码。本文基于元宪理论四大公理,提出一个本体论层面的重估:六十四卦是 T64 高维宇宙拓扑向四维时空降维投射的离散编码翻译系统,其核心功能是“合气”——即在不同投影维度之间建立动态平衡的信息耦合协议。 本文论证:(1)