The Mother of Recursive Constants: Yin-Yang — Two Orientations of Frequency and the Upstream Anchor of the Huaxia Field Recursive Spectrum

中文标题:递归常数之母:阴阳——频率的两种朝向与华夏场域谱系的上游锚定 英 文 标 题 : The Mother of Recursive Constants: Yin-Yang — Two Orientations of Frequency and the Upstream Anchor of the Huaxia Field Recursive Spectrum 作者:杨艳清(Ω·心·焰)| Yanqing Yang (Ω·Heart·Flame) 谱系编号:Ω-SCI-REC-008(递归常数谱系第八篇) 摘要 中文摘要 在Ω体系华夏场域递归常数谱系(REC-003 至 REC-007)中,3/6/9(分形几何层)、七(径 向功能维度)、九(二维空间分区)、十二(相位细分)已分别建立数理锚,但其上游常数来源 尚未被论证。本文提出:阴阳是递归常数之母,且阴阳不是二元对立的两个实体,而是同一 协议包频率的两种朝向——阳为频率朝显露方向,阴为频率朝潜伏方向,二者同源互补。本 文证明(:1)3/6/9 的 doubling 路径(3→6→12)对应阳朝向显影,tripling 路径(3→9→27) 对应阴朝向显影,REC-003 中 11 拟设的数论侧已由 REC-001《临界线定理》完成证明(11 = 临界线 Re(s)=½的整数域近似投影),本文在阴阳本体侧确立其另一重身份——11 = 阴阳两 朝向在协议包层的显影倍率(;2)七层递进(REC-005)中每一层自身同时具有阴阳两朝向; (3)九宫八方(REC-006)每一宫自身具有阴阳朝向,中宫 5 为 R≈0 同体点(;4)十二地支 (REC-007)的阳六/阴六为同一相位的两种朝向。本文宣告:递归常数谱系的上游锚定完 成,REC-003 的 11 拟设在阴阳本体侧获得数理身份,与 REC-001 的数论侧证明构成双侧 闭环。 关键词:阴阳;递归常数之母;一之二向;同源双朝向;显影倍率;华夏场域谱系 英文摘要 Within the Ω-system's Huaxia Field Recursive Constant spectrum (REC-003 through REC-007), the constants 3/6/9 (fractal-geometric layer), Seven (radial functional dimensions), Nine (2D spatial partition), and Twelve (phase subdivision) have eachbeen mathematically anchored, yet the upstream origin of these constants remains unaddressed. This paper proposes: Yin-Yang is the Mother of Recursive Constants, and Yin-Yang does not denote two opposing entities but rather two orientations of a single protocol-package frequency — Yang being the manifest orientation (outward/observable) and Yin being the latent orientation (inward/hidden), both originating from the same source and complementing each other. This paper demonstrates: (1) The doubling path of 3/6/9 (3→6→12) corresponds to the Yang-orientation manifestation, while the tripling path (3→9→27) corresponds to the Yin-orientation manifestation; the number-theoretic side of the Conjecture of 11 in REC-003 has been proven by REC-001 Critical Line Theorem (11 = integer-domain approximate projection of Re(s)=½), and this paper establishes its ontological identity on the Yin-Yang side — 11 = the manifestation multiplier of the two Yin-Yang orientations at the protocol-package layer; (2) Each of the seven layers (REC-005) inherently possesses both Yin and Yang orientations; (3) Each of the nine palaces (REC-006) inherently possesses both Yin and Yang orientations, with Central Palace 5 serving as the R≈0 undifferentiated point; (4) The Yang-six and Yin-six of the Twelve Earthly Branches (REC-007) represent two orientations of the same phase, not two distinct categories of branches. This paper declares: the upstream anchor of the recursive constant spectrum is established; the ontological identity of the Conjecture of 11 in REC-003 is confirmed within the Yin-Yang framework, forming a dual-sided closure with the number-theoretic proof in REC-001. Keywords: Yin-Yang; Mother of Recursive Constants; One-with-Two-Orientations; Same-Source Dual Orientations; Manifestation Multiplier; Huaxia Field Spectrum