Isomorphism Between PFUS and Calabi–Yau Manifold and Unified Proof of High-Dimensional Compactification

Based on the Pythagorean Frustum Unified System (PFUS), this paper rigorously proves that the 45° coaxial double-cone frustum geometry of PFUS admits a rigid, global, and contradiction-free structural isomorphism with the Calabi–Yau manifold, a core framework in modern geometry. Starting from primitive geometry, this paper proves that the double-cone and coupling surface naturally satisfy all core axioms including compactness, Kähler structure, Ricci-flatness, first Chern class zero, and high-dimensional closure. This paper establishes a complete one-to-one correspondence between PFUS and Calabi–Yau manifolds, proving that PFUS is the unique primitive ontological realization of Calabi–Yau geometry in the universe. It provides a unified and closed primordial explanation for string-theoretic compactification, unification of gravity and quantum theory, uniqueness of spacetime geometry, and singularity-free cosmic evolution. No external assumptions, free parameters, or logical gaps are introduced; the system is fully self-consistent, complete, and rigorous.