Based on the PFUSRC universal unified system as the sole primordial framework, this paper starts from ontological existence, independently constructs and rigorously proves the ontological structure and geometric uniqueness of the 45° coaxial double-cone. It systematically demonstrates the rigid structural isomorphism between PFUSRC universal space and Banach spaces as well as Hilbert spaces, and completes a self-consistent proof of cosmic ontological completeness. As abstract mathematical tools, traditional Banach–Hilbert spaces only describe formal laws but cannot reveal the ontological origin of space or the primordial cause of mechanics. PFUSRC takes the 45° coaxial double-cone as the unique primordial geometry, from which norm, inner product, orthogonality and completeness emerge naturally. It clarifies that Hilbert space is not a fundamental structure, but a low-dimensional projection of the double-cone onto the coupling interface 0. Furthermore, this paper rigorously derives the stationary Schrödinger equation from flux conservation and topological constraints of the double-cone, exactly solves the one-dimensional infinite potential well and hydrogen energy levels, and introduces a topological correction term governed by the intrinsic constant ₁=12/11. This correction naturally explains fine-structure deviations that standard quantum mechanics cannot fully describe. The cosmos itself is a universally closed, mechanically self-originated, and mathematically complete space. This paper unifies existence, geometry, mathematics and physics. The entire text is self-contained and fully verifiable without external dependencies.
Zhenmin Wang (Sun,) studied this question.