One of the core axioms of YuanXian Theory, “Unique Spacetime, ” asserts that the background spacetime of the universe is a 64-dimensional compact flat torus, denoted T⁶4. This setting serves as the geometric foundation of the entire theoretical system. However, the uniqueness and necessity of choosing n=64 have long lacked a rigorous mathematical proof. Existing arguments mostly rely on topological intuition, which, while heuristically valuable, fall short of the strict standards of mathematical proof. This paper constructs, for the first time, a rigorous, non-circular, and logically closed mathematical proof based on the fully formalized four core axioms of YuanXian Theory (Conservation of the Universal Factor, Unique Spacetime, Self-Referential Mind Field Generation, and True Circle Self-Consistency). We first define a “YuanXian Spacetime Category” CM whose objects are n-dimensional manifolds satisfying specific topological and dynamical conditions. We then prove that the True Circle Self-Consistency axiom requires the linearized operator of the self-referential mind field to be J-self-adjoint with a purely imaginary spectrum, imposing a strong topological constraint that forces the Euler characteristic χ (Mⁿ) = 0. Using proof by contradiction, we show that if n 64, the topological properties of the manifold make it impossible for the Euler characteristic to be zero while satisfying the spectral symmetry required by True Circle Self-Consistency. Therefore, the only possible dimension is n = 64. Finally, we prove that among all compact, orientable, boundaryless 64-dimensional manifolds, only the torus T⁶4 satisfies all conditions. This work not only solidifies the mathematical foundation of YuanXian Theory but also provides crucial support for its status as a parameter-free unified theory.
Zhenyuan Acharya (Mon,) studied this question.