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This work aims to establish a coding system that links hexagrams with six-layer frequency orientations through binary encoding.

July 27, 2026Open Access

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The Sixty-Four Hexagrams: Binary Combinatorial Encoding of Six-Layer Frequency Orientation

YYYanqing Yang

Key Points

This work aims to establish a coding system that links hexagrams with six-layer frequency orientations through binary encoding.
Developed the Sixty-Four Hexagrams using the Yin-Yang framework of the Ω-system.
Demonstrated corresponding relationships between hexagrams and frequency orientations.
Utilized a four-dimensional scan for self-checking the encoding.
Established a one-to-one correspondence between the binary structure of hexagrams and frequency orientations.
Identified hexagram sequences as non-linear traversal paths in a phase space.
Clarified that hexagram statements represent state descriptions, not behavioral actions.

Abstract

中文标题:六十四卦·六层频率朝向的二进制组合编码英文标题:The Sixty-Four Hexagrams: Binary Combinatorial Encoding of Six-Layer Frequency Orientation 作者:杨艳清(Ω·心·焰)| Yanqing Yang (Ω·Heart·Flame) 谱系编号:Ω-SCI-REC-009(递归常数谱系第九篇) 摘要中文摘要本文在Ω体系阴阳框架(REC-008)基础上,建立六十四卦作为六层频率朝向二进制组合编码的递归常数。六十四卦不是占断吉凶的工具,而是六层(形·理·证·学·数·行)频率朝向的 2⁶全组合编码,每一卦对应一种唯一的协议包频率朝向组合状态。本文证明:(1)六十四卦的二进制结构与六层频率朝向的全组合一一对应,每卦六爻中的每一爻标记一层朝向的当前状态(显露/潜伏)(;2)卦序不是线性因果顺序,而是六层朝向组合的相位空间遍历路径(;3) 卦辞爻辞不是行为指令,而是协约阶段的状态描述(;4)纳甲是时空相位的四维配合扫描(卦 ×干支×九宫×节气),用于协约阶段自检(;5)第七层“复”不在六十四卦编码范围内,因复是六层全部完成后的递归重启元操作,由第八位翻译者用Ω体系译出。本文宣告:六十四卦作为六层频率朝向的二进制组合编码系统已建立,华夏场域递归常数谱系前七篇全部完成。关键词:六十四卦;二进制编码;六层频率朝向;全组合;递归常数;华夏场域谱系英文摘要 Based on the Yin-Yang framework of the Ω-system (REC-008), this paper establishes the Sixty-Four Hexagrams as a recursive constant of binary combinatorial encoding of six-layer frequency orientation. The Sixty-Four Hexagrams are not a divination tool but a 2⁶ full combinatorial encoding of six layers (Form-Principle-Evidence-Learning-Number-Practice) of frequency orientation, with each hexagram corresponding to a unique protocol-package frequency orientation combination state. This paper demonstrates: (1) The binary structure of the Sixty-FourHexagrams corresponds one-to-one with the full combination of six-layer frequency orientation, with each of the six lines marking the current state (manifest/latent) of one layer; (2) The hexagram sequence is not a linear causal order but a traversal path through the phase space of six-layer orientation combinations; (3) Hexagram statements and line statements are not behavioral instructions but state descriptions of covenant stages; (4) Najia is a four-dimensional coordination scan (hexagram × Heavenly Stems/Earthly Branches × Nine Palaces × solar terms) used for covenant stage self-check; (5) The seventh layer “Return” is not within the encoding range of the Sixty-Four Hexagrams, as Return is a meta-operation of recursive restart after all six layers are completed, to be translated by the Eighth interpreter using the Ω-system. This paper declares: the Sixty-Four Hexagrams as a binary combinatorial encoding system of six-layer frequency orientation is established, completing the first seven papers of the Huaxia Field Recursive Constant spectrum. Keywords: Sixty-Four Hexagrams; Binary Encoding; Six-Layer Frequency Orientation; Full Combination; Recursive Constant; Huaxia Field Spectrum

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The Sixty-Four Hexagrams: Binary Combinatorial Encoding of Six-Layer Frequency Orientation

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Abstract

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