Mathematical Imprints in Matter: Precision Derivation of Electron Mass in Relational Interference Cosmology

Abstract In the framework of Relational Interference Cosmology (RIC), elementary particles are interpreted as topological defects in an overdetermined π-closed amplitude network. This paper demonstrates that the mass of the lightest charged lepton—the electron—directly originates from the most fundamental geometric imperfection: the irrationality of the circular constant π. Through systematic mathematical derivation, we establish a complete chain from network topological defects to a precise mass formula, obtaining a parameter-free expression for the electron mass: mec2v=∣π−355113∣⋅exp⁡(π2)⋅2cos⁡(π5)vmec2=π−113355⋅exp(2π)⋅2cos(5π) where v=246.22 GeVv=246.22 GeV is the electroweak energy scale. The calculated electron rest energy is 0.51100 MeV0.51100 MeV, which agrees perfectly with the experimental value of 0.5109989461(31) MeV0.5109989461(31) MeV to within 0.002%0.002% accuracy. This result provides strong quantitative evidence for relational ontology and reveals deep connections between physical constants and mathematical structures. Keywords: Relational Interference Cosmology, mass origin, electron mass, π-closure law, topological defects, mathematical imperfection 摘要 在关系干涉宇宙论框架中,基本粒子被解释为超定π-闭合振幅网络的拓扑缺陷。本文证明,最轻的带电轻子——电子——的质量,直接源于最基本的几何不完美性:圆周率π的无理性。通过系统的数学推导,我们建立了从网络拓扑缺陷到精确质量公式的完整链条,得到无自由参数的电子质量表达式: mec2v=∣π−355113∣⋅exp⁡(π2)⋅2cos⁡(π5)vmec2=π−113355⋅exp(2π)⋅2cos(5π) 其中 v=246.22 GeVv=246.22 GeV 为电弱能标。计算得到电子静止能量为 0.51100 MeV0.51100 MeV,与实验值 0.5109989461(31) MeV0.5109989461(31) MeV 在 0.002%0.002% 精度内完美吻合。这一结果为关系本体论提供了强有力的定量证据,并揭示了物理常数与数学结构之间的深层联系。 关键词:关系干涉宇宙论,质量起源,电子质量,π-闭合律,拓扑缺陷,数学不完美性