Theory of Mid Integration 中道积分理论

This paper establishes the Theory of Mid Integration, a new independent branch of analytic mathematics. Originating from the commutative non-associative complexified 3D numbers C³, it addresses the multi-valued ambiguity of contour integrals of multiple products in symmetric-breaking algebras, and provides a standardized definition of integration, deviation quantification, and geometric degeneration tools. The framework extends naturally to octonions, Jordan algebras, and Clifford algebras. The core construction is the arithmetic mean of all integral branches as the unique standard mid-integral, with deviations quantified by contour integrals of associators and commutators, and classical degeneration on isotropic light cones. We present narrow and generalized mid-integration, deviation decomposition, deviation conservation law, isotropic degeneration theorem, a universal branch enumeration algorithm, and cross-domain applications. Keywords: mid integration; symmetric breaking; non-associative algebra; associator; commutator; isotropic degeneration; octonions; Riemann hypothesis 摘要 本文建立中道积分(Mid Integration)