Isomorphism Between PFUS and Unitary Group / Unitary Transformation and Proof of Quantum 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 unitary group and unitary transformation, the central mathematical framework of modern quantum mechanics. Starting from primitive geometry, this paper proves that the PFUS coupling surface naturally forms a complex structure with inner product space, and transformations driven by the global operator β₁—including phase shifts, structural rotations, and dimensional coupling—strictly preserve inner product, norm, and probability conservation, fully satisfying all axioms of unitarity. This paper establishes a complete one-to-one correspondence between PFUS and the unitary group/unitary transformations, proving that PFUS is the unique primitive ontological realization of quantum unitarity in the universe. It provides a unified and closed primordial explanation for quantum state evolution, probability conservation, symmetry invariance, wavefunction normalization, and the unification of quantum theory and gravity. No external assumptions, free parameters, or logical gaps are introduced; the work is complete, rigorous, and fully self-consistent.