Abstract

This paper introduces the Expansion Theorem of Shinichi Mathematics, a novel mathematical framework that begins with the axiomatic structure √1 = 0 and redefines foundational concepts such as number, ratio, and emergence. The paper formalizes a series of laws including: the Infinite Ratio Transformation Law, the Root-N Conversion Method, the Root-N Dynamic Method, the Squared Total Ratio Transformation Law, and the Shinichi Theorem — all of which describe how the entity "1" can be structurally decomposed and recomposed through abstract combinatorial and geometric relationships. These theorems present a new view of unity and structure beyond conventional mathematical systems.