Mathematical Construction of the Normalization Factor in Yuanxian Theory and the Topologically Isomorphic Schrödinger Equation

In conventional quantum mechanics the normalization of the wave function relies on a probability interpretation imposed by an external observer. This external constraint leaves an unbridgeable logical fissure at the meta-theoretical level of modern physics. Based on the \(\mathcal{T}^{64}\) dimensional-reduction dynamical closed-loop system of Yuanxian Theory, the present paper rigorously constructs a global normalization factor \(N\) and proves that the factor is not an externally appended constraint but an endogenous global calibration coefficient that arises when the 64-dimensional topological source structure is projected onto lower-dimensional space. Starting from the three core laws, the paper completes a rigorous mathematical derivation of the normalization factor along three independent paths—of which the third (non-trivial-zero expansion of the partition function) yields \(N\approx 1.9\times 10^{4}\) from first principles—and obtains the closed expression \(N=[\alpha^{2}(1-\alpha)]^{-1}\approx 18916.91\), which is fully consistent with the core numerical anchors 64-35-137. The paper further reveals the endogenous binding relation between the normalization factor and the wave function: both originate from the same 64-dimensional self-referential mind field, evolve synchronously through the 35-step dimensional-reduction iteration, are jointly calibrated inside the 68-step self-check closed loop, and finally phase-lock at the fine-structure-constant anchor 137. On the basis of this binding relation a topologically isomorphic Schrödinger equation (in discrete eigen-equation form) that is strictly consistent with the 68-step discrete period is constructed; all parameters are rigidly derived from the anchors 64-35-137 and no external free parameters remain. The ontological steady-state solution, the convergence of the dimensional-reduction limit and the anchoring of the fine-structure constant are all verified for self-consistency. The paper demonstrates that normalization is not an external imposition but an endogenous reading of the self-referential metabolism of the cosmic living organism. --- 传统量子力学中的波函数归一化依赖于外部观测者人为设定的概率诠释,这一外部约束在现代物理学的元理论层面留下了不可弥合的逻辑裂隙。本文基于元宪理论\(\mathcal{T}^{64}\)降维动力学闭环体系,严格构造了全域归一化因子\(N\),证明该因子并非外部附加约束,而是64维拓扑本源结构向低维空间投影时内生的全局校准系数。从三大核心规律出发,本文通过三条独立推导路径——其中第三条(配分函数非平凡零点展开)从第一性原理给出\(N\approx 1.9\times 10^{4}\)—完成归一化因子的严格数理推导,其闭合表达式\(N=[\alpha^{2}(1-\alpha)]^{-1}\approx 18916.91\)与64-35-137核心数理锚点完全自洽。进一步地,本文揭示了归一化因子与波函数的内生绑定关系——二者同根生于64维自指心场,在35步降维迭代中同步演化,在68步自检闭环中联动校准,最终在137精细结构常数锚点处锁相收敛。基于此绑定关系,本文构造了与68步离散周期严格自洽的拓扑薛定谔方程(离散本征方程形式),所有参数均由64-35-137锚