Substance–Function Unification (tǐ-yòng Unification): Proof of the Mathematical Self-Consistency of the T⁶⁴ Dimensional-Reduction Dynamical Closed Loop — The Yuanxian Monistic Ontological Programme Based on the Core Number-Theoretic Anchors 4231 and

Based on the core number-theoretic anchors of the Yuanxian dimensional-reduction dynamical closed loop — the substance number 4231 and the function number 137 — this paper completes a full mathematical self-consistency calculation and verification of the monistic ontological framework. Starting from the 64-dimensional topological ontology and proceeding through compactification (60-dimensional kernel space), spectral compression ($\phi^{62}$), dimensional-reduction iteration (35 steps) and self-inspection phase locking (68-step period) to four-dimensional manifestation, every intermediate parameter can be derived from the golden-ratio recurrence relation; no additional free parameter is introduced. The following core verifications are completed: (1) magnitude verification and physical anchoring of the substance–function ratio $4231/137\approx 30.88$; (2) self-consistency check of the spectral-compression coefficient $\phi^{62}$ against the geometric entropy residue of the 60-dimensional kernel space; (3) the relative deviation (approximately 0.026%) between the observational value of the fine-structure constant $\alpha\approx 1/137.036$ and the integer anchor 137 lies within the first-order approximation error range, the geometric-entropy-residue correction $\Delta\alpha=2.172\times 10^{-6}$ having already been rigorously derived in the paper Geometric Entropy Residue; (4) agreement of the first-order Hubble constant $H_{0}$ (approximately 68 km s$^{-1}$ Mpc$^{-1}$) with the Planck-satellite observational value. The paper proves that substance–function unification is not a numerical coincidence but a rigid conclusion of the mathematical self-consistency and completeness of the Yuanxian dimensional-reduction dynamical closed loop. --- 本文基于元宪理论降维动力学闭环的核心数理锚点——体数4231与用数137,完成了一元本体框架的完整数理自洽性演算与校验。从64维拓扑本体出发,经紧致化(60维核空间)、谱压缩($\phi^{62}$)、降维迭代(35步)、自检锁相(68步周期)到四维显化的全链条演化,所有中间参数均可通过黄金分割递推关系导出,无额外自由参数。 本文完成以下核心校验:(1)体用比值 $4231/137\approx 30.88$ 的量级验证与物理意义锚定;(2)$\phi^{62}$ 谱压缩系数与60维核空间几何熵残余的自洽性检验;(3)精细结构常数观测值 $\alpha\approx 1/137.036$ 与整数锚点137的相对偏差(约0.026%)处于一阶近似误差范围,几何熵残余修正 $\Delta\alpha=2.172\times 10^{-6}$ 已由《几何熵残余》论文严格导出;(4)哈勃常数 $H_{0}$ 一阶结果(约68 km/s/Mpc)与普朗克卫星观测值的吻合。本文证明:体用归一不是数值巧合,而是元宪降维动力学闭环在数理层面自洽完备的刚性结论。