3.1 ℳ Field Normal Geometry Structure

Abstract

This article defines the normal geometry structure of the Matter Sector ℳ. The ℳ sector corresponds to the Cl(0)→Cl(3) segment of the Coding Orbit, whose algebraic foundation is the Semisimple Splitting Cl(3) ≅ ℍ ⊕ ℍ. The normal geometry of the Matter Sector is described by the sphere, with radius locked by the Interlock Constants. The two direct summands of the Semisimple Splitting correspond to left-handed and right-handed helicity of matter. This article further provides the geometric realization of Cl(3) ≅ ℍ ⊕ ℍ, the detailed construction of the normal projection operator, and the algebraic definition of the Mass Operator , laying the foundation for mass generation dynamics.