Isomorphism between the Pythagorean Frustum Unified System (PFUS) and the Geometric Framework of Yau's Conjecture and the Complete Theory of 4-Dimensional Dimension Fusion Thresholds

Yau’s Conjecture establishes the equivalence between Kähler–Einstein metrics and K-stability on compact Fano Kähler manifolds with positive first Chern class, forming the core of modern high-dimensional geometry and string compactification, supported by topological invariance, equilibrium metrics, stability and high-dimensional closure. PFUS takes the 45° coaxial double-cone frustum as the unique intrinsic geometry of the universe, establishes the rigid path 1⇒5⇒11, and realizes self-stabilization, self-protection and self-closure via β₁ and π₁=12/11, forming an axiomatic primitive geometric system without external parameters or singularities. This paper presents all axioms of PFUS, proves its structural equivalence with Yau’s Conjecture in four aspects, gives 4D dimension fusion threshold formula and stable dimension interval criterion, clarifies the boundary between primitive theory and engineering practice, and achieves complete closure and correspondence between primitive geometry and modern high-dimensional geometric framework.