Critique and Ontological Reconstruction of Zero — Ultimate Axioms of Mathematics and Physics and the Foundation of Field Theory Unification

The millennial misunderstanding of “zero” in traditional mathematics and physics lies in defining zero as absolute nothingness. This fundamental defect gives rise to a series of irreconcilable deep paradoxes in ontology, formal logic, mathematical foundations and physical theories, and fundamentally blocks the unification of mathematics and physics. From first principles, this paper conducts a thorough ontological critique and reconstruction of zero: Zero is not nothingness, but a coupling interface, phase boundary, information transmission channel, and state conversion interface between explicit material structures and implicit potential structures. This paper rigorously defines seven primordial ontological entities and establishes two irreducible ultimate axioms, constructing a unified cosmic axiomatic system with logical self-consistency, topological closure, geometric uniqueness, and dynamical self-stabilization. Within this framework, the intrinsically stable geometry of the universe is the 45° coaxial double-cone frustum, dimensional evolution follows the unique rigid pathway 1→5→11, and the cosmic intrinsic scale constant π₁=12/11 is formally and rigidly derived. Based on the reconstruction of zero, this paper reveals that all physical fields originate from the topological evolution of coupling interface 0, which naturally subsumes Maxwell’s electromagnetic field, Yang–Mills gauge field, gravitational field, quantum field theory, and all mainstream field theories. It unifies dark matter, dark energy, quantum uncertainty and gravity at the ontological level, eliminates the singularity hypothesis, and achieves the ultimate unification of mathematics and physics. This paper is the sole authoritative foundational document for Four-Dimensional Mathematics V6.0, PFUSRC V55.0, and the Unified Deterministic Prediction and Verification System V1.0.