Based on PFUS, this paper rigorously proves the rigid structural isomorphism between PFUS and Banach-Hilbert spaces. Taking the 45° coaxial double-cone frustum as the unique primitive geometry, PFUS inherently satisfies all definitions of Banach spaces, and is highly consistent with the inner product, orthogonality and basis completeness of Hilbert spaces on the coupling surface. Through axiom review, definition correspondence, theorem derivation and completeness proof, this paper establishes one-to-one correspondence between PFUS and Banach-Hilbert spaces, proving that PFUS is a primitive complete space model without parameters, assumptions or paradoxes, providing a unified and self-consistent explanation for the mathematical nature of the universe.
Zhenmin Wang (Thu,) studied this question.