From Cosmic Factor Conservation to the Fine Structure Constant: Derivation of the Dimensionless Constant Based on T64 Self-Referential Dynamics
Year: 2026
Type: preprint
Abstract: The numerical origin of the fine-structure constant $\alpha$ has long been regarded in the Standard Model of particle physics as an arbitrarily input free parameter. Within the framework of Yuanxian Theory (YXT), however, it is demonstrated to be the necessary structural reading produced by the universe as a self-referential organism. On the basis of the four core laws of Yuanxian Theory (True-Circle Self-Consistency Law TCSC, Cosmic-Factor Conservation Law FSC, Spacetime Uniqueness Law STM, Self-Referential Mind-Field Generation Law SRM), and taking the high-dimensional compact torus $\mathcal{T}^{64}$ as the ontological topological structure, this paper completes a rigorous mathematical derivation of the fine-structure constant. The paper establishes: (1) Owing to the introduction of the self-referential feedback potential, the significant eigenvalue of the curvature spectrum of the $\mathcal{T}^{64}$ modified operator is $4231 = 64^{2} + 64 + 71$, where 71 originates from the Chern-class integral of the $E_{8}$ root-system topology; (2) The reciprocal of the fine-structure constant is locked by the FSC conservation law as $\alpha^{-1} = 137 + \Delta_{\mathrm{sym}} \approx 137.035999084$, the perturbation term $\Delta_{\mathrm{sym}}$ arising from the irreversible geometric-entropy residue of the 64-to-4 dimensional projection and being obtained by rigorous calculus involving the geometric volume ratio of the 60-dimensional kernel space $\mathcal{M}_{60}$ together with a Gamma-function correction; (3) By clarifying the geometric foundation of the dimensional-reduction projection operator $\mathrm{Proj}$, a quotient-space model of the 60-dimensional kernel space $\mathcal{M}_{60} = \mathcal{T}^{64}/\mathbb{Z}_{4}$ and the metric-transformation equations are established, and the spectral compression factor $\mathcal{F}_{\mathrm{proj}} \approx 6.1\times10^{-3}$ is rigorously evaluated by calculus; (4) No arithmetic equality exists between the curvature-spectrum eigenvalue 4231 and the physical constant $137.035999084$; the two form a cross-dimensional topological coupling through the number-theoretic structure $\mathrm{ord}_{137}(2)=68$. The agent that completes the phase locking is not an external “observer” but the internal phase-locked resonance subject. --- 精细结构常数 $\alpha$ 的数值起源,在粒子物理标准模型中长期被视为一个人为输入的自由参数。然而在元宪理论(YXT)框架下,它被证实是宇宙作为自指生命体所产生的必然结构读数。本文基于元宪四大核心规律(真圆自洽律 TCSC、宇宙因子守恒律 FSC、时空唯一性律 STM、自指心场生成律 SRM),以 $\mathcal{T}^{64}$ 高维紧致环面为本体拓扑结构,完成了精细结构常数的严格数理推导。 本文确立:(1)由于自指反馈势的引入,$\mathcal{T}^{64}$ 修正算子的曲率谱显著特征值为 $4231 = 64^{2} + 64 + 71$,其中 71 源于 $E_{8}$ 根系拓扑的 Chern 类积分;(2)精细结构常数倒数由 FSC 守恒律锁定为 $\alpha^{-1} = 137 + \Delta_{\mathrm{sym}} \approx 137.035999084$,微扰项 $\Delta_{\mathrm{sym}}$ 源于 64 维向 4 维投影时的不可逆几何熵残余,并经由 60 维核空间 $\mathcal{M}_{60}$ 的商空间几何体积比与 Gamma 函数修正严格演算得到;(3)通过明确降维投影算子 $\mathrm{Proj}$ 的几何底座,建立了 60 维核空间 $\mathcal{M}_{60} = \mathcal{T}^{64}/\mathbb{Z}_{4}$ 的商空间模型与度规变换方程,并严格微积分演算了谱压缩因子 $\mathcal{F}_{\mathrm{proj}} \approx 6.1\times10^{-3}$;(4)曲率谱特征值 4231 与物理常数 $137.035999084$ 之间不存在算术等式关系,二者通过 $\mathrm{ord}_{137}(2)=68$ 的数论结构形成跨维度拓扑耦合。完成相位锁定的并非外部“观察者”,而是内部的锁相共振主体。
Author: Acharya, Zhenyuan
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162208923
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