This paper establishes the complete, unified, and logically closed four-dimensional mathematical system (V6 Series) on the foundational basis of the critique and reconstruction of zero. It strictly follows four foundational axioms: Fundamental Unity, Four-Dimensional Closure, Algebraic Closure, and Unique Valuation. Primordial 1 generates four spiral motions: left rotation, right rotation, expansion, contraction, which correspond to addition, subtraction, multiplication, and division. Left-right spirals engage in occlusion, self-rotation, and resultant force; up-down spirals govern expansion and contraction to stabilize the four-dimensional unit ₄F. The system satisfies commutativity, associativity, distributivity, identity elements, and null elements. This system unifies definitions, operations, sets, structures, phases, coupling, cycles, and geometric expressions into one self-consistent framework. It is a pure mathematical system that does not depend on physical hypotheses and serves as the necessary and sufficient mathematical foundation for the Pythagorean Primary Substance System V14.0.
Zhenmin Wang (2026) studied this question.