The Triality of SO(8) and the Dimensional Composition-Decomposition Spectrum in Field Topodynamics

Abstract

This paper formalizes the mathematical bridge between the zenith of maximal symmetry in eight dimensions—governed by the Triality property of the SO(8) group—and the operative phenomenology of field topodynamics at the four-dimensional threshold (n=4). We introduce the formalism of dimensional composition and decomposition, demonstrating how the fundamental representations of the D_4 group project hierarchically to generate the non-Abelian gauge fields and chiral fermions observed on the base manifold.