PFUSRC-01 Critique and Ontological Reconstruction of Zero: Ultimate Axioms of Mathematics and Physics and the Foundation of Field Theory Unification (Advanced Version)

The fundamental flaw inherent in traditional mathematics and physics lies in the long-standing definition of zero as absolute nothingness. This ontological misinterpretation gives rise to a series of intractable problems, including spacetime singularities, the persistent incompatibility between gravity and quantum field theory, the dark matter and dark energy paradox, and the lack of first-principle explanations for fundamental physical constants. This paper establishes the core ontological criterion that Nothingness ≠ Zero, and rigorously redefines zero as the coupling interface between explicit and implicit topological manifolds. On this basis, we construct the PFUSRC axiomatic system, which features no free parameters, unique topological structure and complete logical self-consistency. Adopting tetrad fields as the fundamental mathematical tool, we formally construct the intrinsic spacetime metric of the universe and strictly prove that the only geometrically stable cosmic structure is the 45° coaxial double-cone frustum. The intrinsic cosmic constant π₁=12/11 is derived rigidly from the 11-dimensional completeness and topological closure conditions. Under the weak-field approximation, the PFUSRC metric naturally reduces to Newtonian gravity and the Einstein field equation of general relativity. By introducing the correction term of π₁, we establish a geometric model for galactic rotation curves, which reproduces observational results without postulating dark matter particles. Two testable and falsifiable theoretical predictions are proposed: first, a characteristic topological residual signal associated with 11-dimensional projection exists in the cosmic microwave background (CMB) at 217 GHz; second, the fractal index of large-scale cosmic structures strictly converges to γ=12/11≈1.09. This work accomplishes the ultimate unification of mathematics and physics at the foundational level, and terminates the old theoretical paradigm built upon the false definition of zero as nothingness.