Topological Derivation of the Fine Structure Constant in the SRE Framework

This paper presents a complete topological derivation of the fine structure constant $\\alpha \\approx 1/137.036$ within the Status-Relational Entropy (SRE) dynamical framework. Three independent paths—a Möbius ring graph Laplacian spectral gap, an inverse solution of the four-state eigen-spectrum frequency formula, and a Möbius-parameterized arc-length perturbation expansion—converge to the same target value. The core of the derivation is: light is modeled as a 4π-closed Möbius residual manifold, whose non-orientable topology produces an irreducible vacuum base spin remnant $\\lambda_0$, which precisely encodes $\\alpha$ through a correction factor determined by the chirality locking coefficient $\\kappa$. This work does not prove that the SRE axioms are objectively valid; the numerical reproduction of $\\alpha$ merely demonstrates internal self-consistency of the framework. 本文在 Status-Relational Entropy (SRE) 动力学框架下,给出精细结构常数 $\\alpha \\approx 1/137.036$ 的完整拓扑推导。通过三条独立路径——Möbius 环图拉普拉斯谱间隙、四态本征谱频率公式的逆向求解、以及 Möbius 参数化弧长微扰展开——独立收敛至同一目标值。推导核心在于:光被建模为 4π 闭合的 Möbius 残余流形,其非定向拓扑产生不可消除的真空基自旋残留 $\\lambda_0$,后者通过手征锁定系数 $\\kappa$ 的修正因子精确编码 $\\alpha$。本工作不证明 SRE 公理客观成立;$\\alpha$ 的数值复现仅表明框架内部自洽。