(摘要 / 简介)
本手稿从纯几何拓扑的视角探讨了粒子质量的起源，为标准模型中依赖光速 (c) 和精细结构常数 (alpha) 等经验参数的现状提供了一种理论替代方案。基于弧几何的 1+2 维环形流形与自倍律 (LSD)，本研究引入了纯几何拓扑阻抗极限 (alpha_{geom}^{-1} \approx 137.041286) 和绝对空间尺度 (c_{geo} = 3 \times 10^8 \text{ m/s})。利用这些几何常数，本文代数推导出了绝对标准化的电子质量基准：M_{arc\_e} \approx 0.510685 \text{ MeV}/c^2。
将此基准与空间不对称投影修正因子 (mathcal{P}) 应用于拓扑折叠矩阵后，本文对基本粒子质量谱进行了重构。所得出的代数矩阵与目前的对撞机经验数据高度吻合，同时系统性地指出了重粒子（如顶夸克和规范玻色子）的测量质量中存在 sim -0.06% 的度量偏移。此外，在 2^6 拓扑本征满射原则的指导下，该框架提出了一种 64 态的拓扑架构。这表明有必要对现有的 62 粒子模型进行数学上的扩展，并在理论上预言了位于极限微观边界的两个隐藏本征态：然磁极 (B_m^0) 与然光极 (B_l^0)。本研究旨在为理论物理学中绝对拓扑演化的概念化提供严谨的数学基础。
Description
This manuscript explores the origin of particle mass through the lens of pure geometric topology, offering a theoretical alternative to the reliance on empirical parameters such as the measured speed of light (c) and the fine-structure constant (a) in the Standard Model.
This manuscript explores the origin of particle mass through the lens of pure geometric topology, offering a theoretical alternative to the reliance on empirical parameters such as the measured speed of light (c) and the fine-structure constant (a) in the Standard Model.
Grounded in the 1+2 dimensional toroidal manifold of Arc Geometry and the Law of Spontaneous Doubling (LSD), the study introduces a pure geometric topological impedance limit (alpha_{geom}^{-1} \approx 137.041286) and an absolute spatial scale (c_{geo} = 3 \times 10^8 \text{ m/s}). Utilizing these geometric constants, an absolute standardized electron mass baseline is algebraically derived at M_{arc\_e} \approx 0.510685 \text{ MeV}/c^2.
By applying this baseline alongside a spatial asymmetrical projection modifier ($\mathcal{P}$) to a topological folding matrix, the fundamental particle mass spectrum is reconstructed. The resulting algebraic matrix aligns closely with current collider data, while systematically indicating a $\sim -0.06\%$ metrological shift in the measured masses of heavy particles (e.g., the Top quark and Gauge bosons).
Furthermore, guided by the 2^6 topological eigen-surjection principle, the framework posits a 64-state topological architecture. This suggests a mathematical extension of the current 62-particle model, theoretically predicting the existence of two hidden eigenstates at the ultimate microscopic boundary: the Ran-Magnetic (B_m^0) and Ran-Light (B_l^0) poles. This work aims to provide a rigorous mathematical foundation for conceptualizing absolute topological evolution in theoretical physics.
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