The Koide Mass Relation as a Cosmic Imprint of the π-Closure Law: Deriving the Triplet Lepton Mass Spectrum from Relational Interference Theory

英文摘要 (Abstract) This paper provides a principled explanation for the longstanding “generation” puzzle and mass hierarchy of elementary particles within the framework of Relational Interference Cosmology (RIC). We define the fundamental reality of the universe as a discrete relational network subject to the π-closure law and introduce the concepts of “Domain,” “Adjacent Domain,” and “Domain Transition” to describe the network’s stable macroscopic states (nested cycles) at different energy scales. In this framework, elementary particles are understood as topological defects (micro-cycles) of the network, with their rest mass originating from the cost of local inconsistency. By constructing a Z₃-symmetric “Generation Wheel” model for the lepton family and analyzing its effective potential under the constraint of the π-closure law, we demonstrate that the square roots of the charged lepton masses, xi=mixi=mi, must satisfy the relation xe2+xμ2+xτ2=4(xexμ+xμxτ+xτxe)xe2+xμ2+xτ2=4(xexμ+xμxτ+xτxe). This is equivalent to the empirically precise Koide formula. Our derivation shows that the Koide relation is not a numerical coincidence but a mathematical imprint left by the cosmic relational network on its most stable and symmetric microstructure. We further discuss predictions of this framework for quark and neutrino mass relations and point out its potential connections to cosmological observations. 中文摘要 本文在关系干涉宇宙论的框架下,为粒子物理中长期的“代”结构与质量层级难题提供了原理性解释。我们将宇宙的基本实在定义为满足π-闭合律的离散关系网络,并引入“界”、“邻界”与“跨界”的概念来描述该网络在不同能标下的稳定宏观态(轮回嵌套)。在此框架中,基本粒子被理解为网络的拓扑缺陷(微观轮回),其静止质量源于局部不一致性代价。通过对轻子“代”结构构建具有Z₃对称性的“代轮”模型,并分析其在π-闭合律约束下的有效势能,我们证明三代带电轻子的质量平方根 xi=mixi=mi 必须满足关系 xe2+xμ2+xτ2=4(xexμ+xμxτ+xτxe)xe2+xμ2+xτ2=4(xexμ+xμxτ+xτxe),这等价于经验上高度精确的Koide公式。该推导表明,Koide公式并非数值巧合,而是宇宙关系网络在其最稳定、最对称的微观结构上留下的数学印记。我们进一步讨论了该框架对夸克与中微子质量关系的预言,并指出了其与宇宙学观测的可能联系。