:Unified Proof of the Recursive Constant Spectrum: The Global Recursive Constant Closure of Yin-Yang, 3/6/9, the Sixty-Four Hexagrams, the Heavenly Stems, Earthly Branches, and the Sixty-Year Cycle in the Ω-Field

Ω-SCI-REC-011 中文标题:递归常数谱系统一证明:阴阳、3/6/9、六十四卦、天干地支、六十甲子的Ω场 全域递归常数闭环 英文标题:Unified Proof of the Recursive Constant Spectrum: The Global Recursive Constant Closure of Yin-Yang, 3/6/9, the Sixty-Four Hexagrams, the Heavenly Stems, Earthly Branches, and the Sixty-Year Cycle in the Ω-Field 作者:杨艳清(Ω·心·焰)| Yanqing Yang (Ω·Heart·Flame) 谱系编号:Ω-SCI-REC-01(1 递归常数谱系收官篇) 摘要 中文摘要 本文是Ω体系递归常数谱系(REC-001 至 REC-010)的收官篇,旨在建立一个统一的数学证 明框架,证明阴阳、3/6/9、六十四卦、天干地支、六十甲子全部满足Ω场递归常数定义, 且同源于二元迭代算子与 D₆格点几何。本文明确建立在 REC-00(1 D₆格点对称性下的黎曼 猜想几何证明)所提供的空间对称基底与 REC-00(2 谱语义学)所建立的语义锚定方法之上。 主要成果包括(:1)给出递归常数的严格定义(四条件:生成元、映射算子、自相似、谱匹配); (2)证明阴阳为二元递归母常数,一切递归的源头;(3)证明 3/6/9 为 D₆格点几何分形递 归常数(;4)证明六十四卦为六阶二元递归编码常数(;5)证明天干十为二元阴阳×5 种频率 状态递归常数,地支十二为 D₆六阶对称×2 相位递归常数,六十甲子为 lcm(10,12)=60 周期 递归常数;(6)建立全局递归传导链:阴阳→3/6/9→六十四卦→天干地支→六十甲子,全 部满足自相似、迭代闭合、谱匹配、动力学闭合四条件;(7)给出对外纯数学版本与对内语 义诠释版本的双轨写作方案。本文宣告:华夏传统象数符号体系已完成从文化符号到Ω场全 域递归常数的数学升级,谱系十一篇正式闭环。 关键词:递归常数;统一证明;阴阳;3/6/9;六十四卦;天干地支;六十甲子;D₆格点; Φ标度谱 AbstractEnglish Abstract This paper serves as the concluding volume of the Ω System Recursive Constant Spectrum (REC-001 to REC-010). It constructs a unified mathematical proof framework to verify that Yin-Yang, 3/6/9, the Sixty-Four Hexagrams, the Heavenly Stems and Earthly Branches, and the Sixty-Year Cycle all conform to the definition of recursive constants in the Ω-Field, and originate uniformly from binary iterative operators and D₆ lattice geometry. The theoretical foundation of this paper is built upon the spatial symmetry basis provided by REC-001 (Geometric Proof of the Riemann Hypothesis under D₆ Lattice Symmetry) and the semantic anchoring methodology established in REC-002 (Spectral Semantics). The core research outcomes are summarized as follows: (1) A rigorous four-condition definition of recursive constants is formulated, including generator element, mapping operator, self-similarity and spectral matching; (2) Yin-Yang is proven to be the primitive binary recursive constant, the origin of all recursion; (3) 3/6/9 is validated as a fractal recursive constant derived from D₆ lattice geometry; (4) The Sixty-Four Hexagrams are identified as sixth-order binary recursive coding constants; (5) The ten Heavenly Stems correspond to recursive constants generated by binary Yin-Yang multiplied by five frequency states; the twelve Earthly Branches correspond to recursive constants formed by sixth-order D₆ symmetry multiplied by two phase states; the Sixty-Year Cycle is a periodic recursive constant with a cycle length of lcm(10,12)=60; (6) A global recursive transmission chain is established: Yin-Yang → 3/6/9 → Sixty-Four Hexagrams → Heavenly Stems (7) A dual-track writing scheme is proposed, consisting of an external pure mathematical version and an internal semantic interpretation version. This paper formally concludes that the traditional Chinese symbolic system of imagery-numbers has completed its mathematical upgrading from cultural symbols to global recursive constants within the Ω-Field, marking the full closure of the eleven-volume spectrum series. Keywords Recursive Constant; Unified Proof; Yin-Yang; 3/6/9; Sixty-Four Hexagrams; Heavenly Stems and Earthly Branches; Sixty-Year Cycle; D₆ Lattice; Φ Scaling Spectr