PFUSRC-51: Rigid Global Isomorphism and Ultimate Unification Proof of PFUSRC with Five Core Structures

This paper presents the definitive proof that the Pythagorean Frustum Unified System – Rigid Canonical (PFUSRC) constitutes the unique ontological structure underlying five foundational pillars of modern mathematics and physics: Kähler–Einstein metrics, K-stability criterion, Fano manifolds, unitary groups and unitary transformations, and general relativistic spacetime. Synthesizing the axiomatic foundations of PFUSRC-00, the structural invariance proofs of PFUSRC-48, the convex optimization framework of PFUSRC-49, the mathematical isomorphism results of PFUSRC-50, and the latest observational constraints from PFUSRC-11, this work establishes a rigid, one-to-one structural isomorphism between the 45° coaxial double-cone frustum geometry and each of these formalisms. No external assumptions, free parameters, or logical loopholes are introduced. The theory resolves long-standing incompatibilities in the standard ΛCDM model, explains key anomalies such as the Hubble tension and large-scale cosmic web structure, and delivers a complete, self-consistent unification of gravity and quantum mechanics. This work confirms that PFUSRC is not merely a mathematical construct but the fundamental ontological blueprint of the universe.