What does this research mean for the field?

The sixty-four hexagrams of the Yijing constitute a discrete encoding translation system projected from a high-dimensional cosmic topology onto four-dimensional spacetime to establish dynamic information-coupling protocols. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

This paper aims to decode the sixty-four hexagrams of the Zhouyi by providing a new ontological framework based on Yuanxian Theory.

June 26, 2026Open Access

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

Key Points

This paper aims to decode the sixty-four hexagrams of the Zhouyi by providing a new ontological framework based on Yuanxian Theory.
Utilized Yuanxian Theory's four axioms to reevaluate hexagrams as a discrete encoding system.
Demonstrated the mapping of the sixty-four hexagrams to topological and temporal sequences.
Incorporated quantitative methods and full-volume hexagram-chain mapping for validation.
The structure of the sixty-four hexagrams corresponds exactly to discrete subgroup Z_2^6 of T64.
Hexagram transformations are shown to represent the projection of T64 dynamics onto temporal sequences.
Established that 'Heqi' manifests as a steady-state dynamic in living and social systems.

Abstract

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 2⁶=64 structure of the sixty-four hexagrams is a precise mirror of the discrete subgroup Z₂⁶ 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) 六十四卦的 2⁶=64 结构是 T64 离散子群 Z₂⁶ 的精确镜像, 卦象是闭链环绕数在低维的符号映射; (2) “卦变”是 T64 闭链动力学在四维时序上的投影轨迹; (3) “合气”是 TCSC 自指迭代在生命/社会系统中的稳态收敛态。本文补充卦象概率闭合解析式、量化实验范式、全量卦链对照数据, 完善可证伪实验体系, 将易学从“玄学”重新定位为“高维拓扑信息的低维符号化协议”, 为中医、风水、命理等传统实践提供了可形式化、可机器验证的元理论底座

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