Critique and Ontological Reconstruction of Zero Ultimate Axioms of Mathematics and Physics and the Foundation of Field Theory Unification (Advanced Version)

The traditional mathematical and physical systems are built on the wrong definition of zero as absolute nothingness, leading to unavoidable contradictions such as spacetime singularities, the unification difficulty of gravity and quantum theory, the puzzles of dark matter and dark energy, and the lack of first-principle explanations for fundamental constants. This paper proposes the strict ontological criterion that Nothingness ≠ Zero, and redefines zero as the coupling interface between explicit and implicit topological spaces. On this basis, the PFUSRC axiomatic system is established with no free parameters, unique topological structure and complete logical consistency. By using tetrad fields, the intrinsic metric of the universe is formally constructed, and the 45° coaxial double-cone geometry is rigorously derived. The cosmic fundamental constant π₁ = 12/11 is obtained from 11-dimensional completeness and topological closure. Under weak-field approximation, the PFUSRC metric naturally reduces to Newtonian gravity, general relativity and Maxwell’s equations. Using the π₁ correction, a geometric model of galactic rotation curves is obtained without introducing dark matter. Two falsifiable predictions are proposed: a characteristic topological signal exists in the CMB at 217 GHz; the fractal index of large-scale cosmic structure is γ = 12/11 ≈ 1.09. This work realizes the ultimate unification of mathematics and physics and replaces the old paradigm based on the misunderstanding of zero.