Isomorphism Between PFUS and Fano Manifold and Proof of Positive-Curvature Cosmic Unity

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 Fano manifold, a core object in modern high-dimensional geometry. Starting from primitive geometry, this paper proves that the upper-cone region of PFUS naturally forms a compact Kähler manifold with strictly positive first Chern class, satisfying all definitions and topological constraints of Fano manifolds. The global operator β₁ and scale factor π₁ jointly maintain stable expansion, balanced closure, and singularity-free evolution of the positive-curvature structure. This paper establishes a complete one-to-one correspondence between PFUS and Fano manifolds, proving that PFUS is the unique primitive ontological realization of Fano geometry in the universe. It provides a unified and closed primordial explanation for the domain of Yau’s conjecture, the origin of positive-curvature cosmology, high-dimensional compactification topology, and spacetime structural stability. No external assumptions, free parameters, or logical gaps are introduced; the work is complete, rigorous, and fully self-consistent.