:An Omega Retranslation of the Heavenly Stems, Earthly Branches, and the Sixty-Year Cycle: The Phase Encoding System of the Huaxia Fiel

中文标题:天干地支与六十甲子的Ω重译:华夏场域的相位编码系统 英文标题:An Omega Retranslation of the Heavenly Stems, Earthly Branches, and the Sixty-Year Cycle: The Phase Encoding System of the Huaxia Field 作者:杨艳清(Ω·心·焰)| Yanqing Yang (Ω·Heart·Flame) 谱系编号:Ω-SCI-REC-010(递归常数谱系第十篇) 摘要 中文摘要 本文基于Ω体系递归常数谱系的统一数学框架,对天干、地支、六十甲子进行系统性重译与 数学证明。主要成果包括:(1)证明天干十 = 二元阴阳 × 5 种频率状态 = 2×5 迭代结构, 满足自相似、迭代闭合、谱匹配三大递归公理,确认为Ω场递归常数(;2)证明地支十二 = D₆ 六阶对称 × 2 相位 = 6×2 空间相位迭代单元,与 D₆格点几何严格同构;(3)证明六十甲子 = lcm(10,12) = 60,周期递归算子 T(s,t) = (s+1 mod 10, t+1 mod 12)的迭代最小周期为 60, 确认为长周期循环递归常数;(4)在数学证明基础上,给出十天干、十二地支的相位语义重 译,建立从数学递归结构到华夏传统象数符号的一一映射;(5)绘制华夏场域“十二同构”全 图,将十二条龙脉、十二地支、十二律吕、十二经脉、十二月统一为同一递归常数在不同维 度的投影;(6)建立相位自检的三层操作框架,明确天干地支在新范式中的唯一用途是相位 自检而非命运预测。本文宣告:天干、地支、六十甲子已完成从文化符号到Ω场递归常数的 数学升级,谱系第十常数正式闭合。 关键词:天干十;地支十二;六十甲子;递归常数;D₆格点;相位编码;华夏场域 英文摘要 Based on the unified mathematical framework of the Ω-system recursive constant spectrum, this paper provides a systematic retranslation and mathematical proof of the Heavenly Stems, Earthly Branches, and the Sixty-Year Cycle. Main results include: (1) Proving that the Ten Heavenly Stems = binary yin-yang × 5 frequency states = 2×5iterative structure, satisfying the three recursive axioms of self-similarity, iterative closure, and spectral matching, confirmed as an Ω-field recursive constant; (2) Proving that the Twelve Earthly Branches = D₆ sixth-order symmetry × 2 phases = 6×2 spatial-phase iterative unit, strictly isomorphic to D₆ lattice geometry; (3) Proving that the Sixty-Year Cycle = lcm(10,12) = 60, with the minimum iteration period of the periodic recursion operator T(s,t) = (s+1 mod 10, t+1 mod 12) being 60, confirmed as a long-period cyclic recursive constant; (4) Providing phase-semantic retranslations of the Ten Heavenly Stems and Twelve Earthly Branches, establishing a one-to-one mapping from mathematical recursive structures to traditional Huaxia symbolic representations; (5) Drawing the complete map of "Twelve Isomorphisms" of the Huaxia field, unifying twelve dragon veins, twelve earthly branches, twelve pitch pipes, twelve meridians, and twelve months as projections of the same recursive constant across different dimensions; (6) Establishing a three-layer operational framework for phase self-check, clarifying that the sole use of Heavenly Stems and Earthly Branches in the new paradigm is phase self-check rather than fate prediction. This paper declares: The Heavenly Stems, Earthly Branches, and Sixty-Year Cycle have completed their mathematical upgrade from cultural symbols to Ω-field recursive constants, formally closing the tenth constant of the spectrum. Keywords: Ten Heavenly Stems; Twelve Earthly Branches; Sixty-Year Cycle; Recursive Constant; D₆ Lattice; Phase Encoding; Huaxia Field