Perfect Correspondence Between PFUS and K-Stability Criteria and Proof of Structural Stability

Based on the Pythagorean Frustum Unified System (PFUS), this paper rigorously proves that the PFUS framework admits a complete, rigid, and contradiction-free one-to-one correspondence with K-stability criteria, a cornerstone of modern high-dimensional geometry. Starting from primitive geometry, this paper shows that PFUS dimensional selection, steady-state conditions, structural closure requirements, and 4D fusion thresholds are fully equivalent to the core criteria of K-stability. The global operator β₁ and scale factor π₁ together supply the intrinsic constraints that prevent collapse, deformation, divergence, and singular behavior. This paper establishes full mathematical equivalence between PFUS and K-stability, proving that PFUS is the unique primitive ontological realization of K-stability in the universe. It provides a unified, closed primordial explanation for Yau’s conjecture, existence of high-dimensional manifolds, uniqueness of spacetime geometry, and cosmic steady-state mechanisms. No external assumptions, free parameters, or logical gaps are introduced; the work is complete, rigorous, and fully self-consistent.