Critique and Ontological Reconstruction of Zero: Foundational Axioms for Mathematics and Physics

The millennial misunderstanding of zero lies in treating it as absolute nothingness, which leads to paradoxes in ontology, logic, mathematics, and physics. This paper fundamentally critiques the traditional conception of zero and reconstructs its ontological meaning: zero is not void, but a virtual intermediate state, a logical boundary, and a transition interface. Three primordial entities are formally defined: primordial being 1, virtual zero 0, and latent base 1⁰. Four foundational axioms are established: Axiom of Fundamental Unity, Axiom of Four-Dimensional Closure, Axiom of Algebraic Closure, and Axiom of Unique Valuation. Primordial 1 generates four fundamental spiral motions—left rotation, right rotation, expansion, contraction—forming the dynamical origin of arithmetic operations. This paper provides the rigorous, self-consistent, irreducible foundation for a unified system of mathematics and physics, and serves as the formal origin of the 6-series mathematical framework and the 14.0 cosmic unified system.