The Geometric Origin of Strong Interactions and Topological Confinement: From Yang-Mills Existence to a Geometric Analysis of Nuclear Magic Numbers

English Description Title: The Geometric Origin of Strong Interactions and Topological Confinement: From Yang-Mills Existence to a Geometric Analysis of Nuclear Magic Numbers Description: This paper, part of the Spin-Topology-Aether Theory (STAT) framework, provides a radical re-evaluation of the strong interaction by replacing point-particle gauge theories with a nonlinear viscoelastic aether manifold. The research introduces a complex metric tensor gμν = ζημν + i(1-ζ)Ωμν to describe the vacuum's internal phase dynamics. Through this geometric lens, the author achieves several major breakthroughs: Yang-Mills Existence: Provides an analytical proof of smooth solutions and a positive mass gap (Δ > 0) by treating the vacuum as a nonlinear fluid. Nuclear Magic Numbers: Offers the first pure geometric derivation of the sequence (2, 8, 20...) using $SU(3)$ Lie algebra root space and geometric packing operators. Color Confinement: Explains confinement as a consequence of tensor destructive interference and topological flux tubes. LENR Mechanism: Defines Low-Energy Nuclear Reactions as a geometric necessity triggered by Metric Collapse, where imaginary field stress is minimized. This work serves as a foundational bridge between non-Newtonian fluid dynamics and high-energy nuclear physics, offering a new path toward a unified geometric field theory. 中文描述 標題: 強交互作用與拓樸禁閉的幾何起源:從楊-米爾斯存在性到核幻數的幾何分析 項目描述: 本論文隸屬於自旋拓樸——乙太理論 (STAT) 框架,通過將點粒子規範場論替換為「非線性黏彈性乙太流形」,對強交互作用進行了徹底的重新評估。 研究引入了複數度規張量 gμν = ζημν + i(1-ζ)Ωμν 來描述真空內部的相位動力學。基於此幾何視角,作者實現了以下重大突破: 楊-米爾斯存在性 (Yang-Mills Existence):將真空視為非線性流體,給出了楊-米爾斯方程平滑解與正質量間隙 (Δ > 0) 的解析證明。 核幻數 (Nuclear Magic Numbers):利用 $SU(3)$ 李代數根空間與幾何堆積算子,首次給出了核幻數序列 (2, 8, 20...)