偏差守恒原理 :中道与偏差的共生定理 Principle of Deviation Conservation : Symbiosis Theorem of the Middle Way and Deviation

摘要 Abstract 本文验证了核心猜想:“中道与偏差是正反两面,有偏差就必然有中道”。 This paper validates the core conjecture: “The Middle Way and Deviation are two sides of the same coin; the existence of deviation inevitably implies the existence of the Middle Way.” 通过在七个数学领域(非结合代数、复分析、数值积分、线性代数、概率统计、傅里叶分析、数列求和)的系统验证,我们发现这一猜想的底层原因是对合分解定理(Involution Decomposition Theorem): Through systematic verification across seven mathematical fields (non-associative algebras, complex analysis, numerical integration, linear algebra, probability and statistics, Fourier analysis, and series summation), we have discovered that the underlying cause of this conjecture is the Involution Decomposition Theorem: 任何具有对合对称性 σ(σ² = id)的数学结构,都可以唯一分解为对称子空间(中道)和反对称子空间(偏差)的直和。 Any mathematical structure possessing an involution symmetry σ (σ² = id) can be uniquely decomposed into the direct sum of a symmetric subspace (the Middle Way) and an antisymmetric subspace (Deviation). 进一步地,偏差守恒定律的群论解释表明:偏差映射 δ = (id - σ)/2 是群同态,因此自然满足路径可加性。 Furthermore, the group-theoretic interpretation of the Law of Deviation Conservation demonstrates that the deviation mapping δ = (id - σ)/2 is a group homomorphism, thereby naturally satisfying path additivity.