Z-Geometric Dynamics: The Geometric Origin of the Strong Force

Building upon the Z-Geometric Dynamics framework (Papers I, II, and III), this paper further explores the geometric unification of the strong interaction. Employing the seven-dimensional parameter space S^7 as the geometric arena, we utilize its Hopf fibration S^3 ↪ S^7 → S^4 and a three-brane structure to project the SU(3) gauge field from the mixed components of the seven-dimensional spin connection. Through a volume ratio calculation, we obtain the strong coupling constant α_s=32/(9π^3), an expression purely determined by geometry without any free parameters. We establish a "three-lobe excision" model that naturally yields fractional charges and the linear potential of color confinement. Starting from the seven-dimensional Einstein-Cartan equations, we derive an analytic form for the heavy quark potential. This paper is divided into two parts: Part I presents the first-principles derivation of the geometric framework for the strong force; Part II presents phenomenological predictions based on this framework, which involve additional assumptions or empirical parameters whose rigorous derivation is left for future work. All "extra dimensions" refer to a mathematical parameter space describing the internal topological structure of particles, not physical spacetime dimensions.