Calibration of the Topological Reading Path for the Strong Coupling Constant αₛ(M_Z) — Elimination of the "Open Failure" Mark in Yuanxian Theory Core Paper No. 7 and the QCD Cross-Section Reading Protocol

Abstract

In Yuanxian Theory Core Paper No. 7, “Reading Paths of the 24 Fundamental Physical Constants” (10.5281/zenodo.22239740), the entry for the strong coupling constant \(\alpha_s(M_Z)\) was the only reading path among the 24 entries that had not yet closed. This paper proposes a calibration scheme for that path. **Core contribution**: We establish a four-step reading-protocol framework from the topological invariants of \(\mathcal{T}^{64}\) to the experimental value of \(\alpha_s(M_Z)\): 1. **Cross-section calibration** — position the reading pointer at the QCD cross-section \(k_{\rm QCD}=36\) (exploratory candidate);2. **Gauge-group structure factor** — \(\mathcal{G}_{\alpha_s}=32/27\), uniquely determined by the ratio of SU(3) Casimir operators;3. **Spectral compression factor** — \(\mathcal{S}=[\alpha(1-\alpha)]^{-1/64}\cdot\varphi^{-35/64}\);4. **High-energy anchoring and RGE translation** — read out the high-energy value \(\approx1.52\times10^{-4}\) at the locking scale, and propose the complete path of translation to the \(M_Z\) scale via standard RGE (numerical verification pending). **Current status**: The reading-protocol framework has been proposed. The high-energy anchor value, the spectral-geometric derivation of \(\mathcal{S}\), and the group-theoretic evaluation of \(\mathcal{G}_{\alpha_s}\) are completed. The rigorous derivation of the factor 68 and of \(k_{\rm QCD}=36\), as well as the independent verification of RGE numerical consistency, remain open tasks. --- 在元宪理论第七号核心论文《24个基本物理常数的读出路径》(10.5281/zenodo.22239740)中,强耦合常数 \(\alpha_s(M_Z)\) 的条目是常数计算纲领24个条目中唯一未合拢的读数路径。本文提出该路径的校准方案。 **核心工作**:本文建立了从 \(\mathcal{T}^{64}\) 拓扑不变量到 \(\alpha_s(M_Z)\) 实验值的四步读数协议框架: 1. **截面校准** — 将读数指针定位到QCD截面 \(k_{\rm QCD}=36\)(探索性候选);2. **规范群结构因子读取** — \(\mathcal{G}_{\alpha_s}=32/27\),由SU(3) Casimir算子比值唯一决定;3. **谱压缩因子读取** — \(\mathcal{S}=[\alpha(1-\alpha)]^{-1/64}\cdot\varphi^{-35/64}\);4. **高能锚定与RGE翻译** — 在锁定能标处读出高能值 \(\approx1.52\times10^{-4}\),并提出经标准RGE翻译至 \(M_Z\) 能标的完整路径(数值验证待完成)。 **当前状态**:读数协议框架已提出。高能锚定值、\(\mathcal{S}\) 的谱几何推导、\(\mathcal{G}_{\alpha_s}\) 的群论计算均已完成。68因子与 \(k_{\rm QCD}=36\) 的严格推导、RGE数值一致性的独立验证仍为待完成项。