Critique and Ontological Reconstruction of Zero and Physics Fundamental Axioms of Mathematics and Physics

The long‑standing fundamental misunderstanding of the concept of zero within traditional mathematics and physics stems from defining zero as absolute nothingness. This flawed definition gives rise to a series of profound logical paradoxes in ontology, formal logic, mathematics and physical theory. This thesis conducts a systematic and in‑depth critique of the traditional definition of zero, and carries out a thorough ontological reconstruction of its essential connotation. Zero is not equivalent to void or non‑existence in essence; it functions as a coupling interface, a phase boundary, an information transmission channel, and a state conversion boundary between explicit material structures and implicit potential structures. This paper defines seven primitive ontological entities in a rigorous theoretical framework: the One‑All G, Unit‑One, Primordial One 1, Coupling Interface 0, Background‑One 1°, global operator β₁, and dynamic parameter π₁. Two ultimate irreducible fundamental axioms are established in this research: the Axiom of Primordial Unity and the Axiom of Four‑Dimensional Closure. The theoretical connotation of the Five‑Element Rigid Closed Cycle of the universe is integrated into the whole system, clarifying that logical rules occupy the dominant position in the operation of the cosmic system, and the operator β₁ belongs to the derivative category subordinate to logic. This research provides the only formal, standardized and irreplaceable axiomatic theoretical basis for Four‑Dimensional Mathematics V6.0, the PFUS V14.0 system, and the Unified Deterministic Prediction and Verification System V1.0. It lays an irreplaceable ontological theoretical cornerstone for the complete construction of the whole cosmic unified system.