偏元数学与中华玄学底层编码系统的双向映射——当减法不能清零的公理在太极、河洛、八卦、五行、干支中找到了自己的签名 (A Bidirectional Mapping Between Partial-Deviation Mathematics and the Underlying Encoding System of Chinese Ancient Metaphysics: When the Axiom of Subtraction Non-Closure Finds Its Signature in Taiji, Heluo, Bagua, Wuxing, and the Heavenly Stems and Earthly Branches)

本文尝试在偏元数学(Partial-Deviation Mathematics, PDM)与中华玄学底层编码系统(太极、阴阳、五行、河图洛书、八卦、六十四卦、天干地支)之间建立系统性双向映射。偏元数学以减法不可闭性为核心公理——任何自指操作都会留下一个不可约的非零残差ε。本文提出:古人创立太极、阴阳、五行、河洛、八卦、干支等符号系统时,其认知底层被同一种宇宙方向偏好的签名所驱动。这个签名的数学名称是δ₀,量级约为10⁻⁶⁰。这不是用2026年的数学去解释古人的智慧,而是为古老符号系统中那些长期被视为“不完美”的结构(先天方图的不对称、太极图的不完全对称、河洛差值10等)找到了一个精确的数学签名。本文不依赖任何物理常数或观测,仅从偏元数学公理出发,与上古符号体系生成结构上的对应。 This paper attempts to establish a systematic bidirectional mapping between Partial-Deviation Mathematics (PDM) and the underlying encoding system of Chinese ancient metaphysics (Taiji, Yin-Yang, Five Elements, River Map, Luo Book, Eight Trigrams, Sixty-Four Hexagrams, Heavenly Stems and Earthly Branches). PDM is centered on the axiom of subtraction non-closure — any self-referential operation leaves an irreducible non-zero residual ε. We propose that when ancient sages created these symbol systems, their cognitive foundations were driven by the same signature of cosmic directional preference. This signature bears the mathematical name δ₀, with a magnitude of approximately 10⁻⁶⁰.