PFUSRC-107 Complete Formulation of Topological Rheology Tensor and Intrinsic Geometric Derivation of Yang–Mills Gauge Fields

PFUSRC-106 established the ontological positioning of 4-dimensional topological flow variables (TFVs) within the global topological hierarchy and set three core framework-hardening objectives: explicit construction of the 4-dimensional topological rheology tensor, intrinsic geometric origin of Yang–Mills gauge fields, and rigorous analytical solution for topological gravitational wave frequencies. As the landmark paper marking the full closure of the main mathematical framework of the PFUSRC system, this paper fulfills all remaining rigorous supplements without introducing any additional axioms. This work first constructs the complete analytical form of the PFUSRC topological rheology tensor T_{PFUSRC }^{\mu \nu}. In accordance with final peer-review mandates, supplementary constraints on tensor symmetry, Hermiticity, positive-definite dominant energy conditions, and topological parity-breaking structures are incorporated to fully resolve concerns regarding the tensor’s physical validity. Second, starting from the steady-state topology of the 11-dimensional triple 45° coaxial bicone, the complete Standard Model gauge group U(1) ⊗SU(2) ⊗SU(3) is intrinsically deduced via hierarchical axial topological breaking. A geometric degree-of-freedom locking mechanism accounts for the uniqueness of fundamental interaction gauge groups, filling a long-standing theoretical gap in modern geometric field theory. Based on the intrinsic \mathbb{Z}_{3} triaxial cyclic duality symmetry of the framework, a general formula for the mass spectrum of three fermion generations is constructed via topological constraints. The global phase ϕ is fixed through topological quantization loop conditions to eliminate any free-parameter ambiguity and achieve fully first-principle mass-spectrum predictions. The intrinsic frequency of topological gravitational waves within the LISA observational band is solved rigorously, paired with signal-to-noise benchmarking against detector background noise to form a complete falsifiable experimental prediction chain. Finally, an irreversible hierarchical subordinate relationship is defined among the PFUSRC tensor, gauge field effective theories, and General Relativity. Upon final revision, the PFUSRC system formally satisfies all criteria for an independent axiomatic physical theory with a fully closed core theoretical framework, enabling equal paradigm-level dialogue with mainstream physics across mathematics, quantum field theory, cosmology, and particle physics.