Reducing the Computational Cost of QED Stability Analysis with SRE Graph Computations: Mechanism, Worked Examples, and Asymptotic Analysis

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Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-16
DOI
https://doi.org/10.5281/zenodo.22787129
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Particle physics theoretical and experimental studies
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article
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article

Reducing the Computational Cost of QED Stability Analysis with SRE Graph Computations: Mechanism, Worked Examples, and Asymptotic Analysis

Yue Lu
Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
article

Reducing the Computational Cost of QED Stability Analysis with SRE Graph Computations: Mechanism, Worked Examples, and Asymptotic Analysis

Yue Lu
article en

Abstract

The core computational task of QED is to answer "can the electron orbit remain stable under perturbation", and its standard implementation is multi-order Feynman-diagram perturbative summation, whose cost grows (roughly) factorially with the required precision. This paper proposes an orthogonal path within the SRE framework: encode "stability" in the spectral response of the 60-node Möbius ladder $M_{60}$, readable from a first-order eigenvalue solve, **aligning only with QED's stability conclusions, not with its computational process**. The argument is threefold. (1) *Mechanism*: "stability" in SRE is expressed by the raw spectral gap $\lambda_2$ and $\mathbb{Z}_2$ double-cover topological immunity. (2) *Worked examples*: for four criteria — immunity, topological (Z₂) breaking, deep-potential disorder, and cross-class ordering — we give a side-by-side computational-cost comparison of QED and SRE; numerical validation passes 4/4. (3) *Asymptotic analysis*: we compare the complexity scaling of multi-order perturbative summation versus spectral solving as a function of the required precision, quantifying "a one-tier reduction of complexity at the criterion layer". The paper honestly states its boundaries: the simplification holds only at the decision layer, not for per-precision numerical prediction; α is treated as a direct input retreat with no emergence claim. QED 的核心计算任务是回答"电子轨道经扰动后能否保持稳定",其标准实现是多阶费曼图微扰求和,计算代价随所需精度指数增长。本文在 SRE 框架下提出一个正交路径:把"稳定性"编码为 60 节点 Möbius 阶梯 $M_{60}$ 的谱回应用一阶特征值求解即可判读,**只对齐 QED 关于稳定性的结论输出,不对齐其计算过程**。本文给出该方法的三层论证:(1) 机理——"稳定性"在 SRE 中由谱间隙 $\lambda_2$(原始谱)与 $\mathbb{Z}_2$ 双覆盖拓扑免疫表达;(2) 算例——对免疫性、拓扑破缺、深势无序、跨类排序四类判据,逐一给出 QED 与 SRE 的计算需求对比;数值验证 4/4 通过;(3) 渐近分析——对比多阶微扰求和与谱求解在所需精度下的复杂度缩放,给出"判据层复杂度下降一个档次"的量化依据。全文诚实地声明适用边界:该简化只在判定性层次有效,不延伸到逐精度数值预言;且 α 系作为直接输入,本文不做 α 的涌现宣称。

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