Instanton Construction of the Yang--Mills Mass Gap --- A Refined Scheme of Yuanxian T64 Theory

Yang-Mills existence and the mass gap problem is one of the seven Millennium Prize Problems designated by the Clay Mathematics Institute. Based on the high-dimensional topological framework of Yuanxian T64 theory, this paper provides a systematic constructive proof of this problem. The core proposition holds that quantum Yang-Mills field theory on a four-dimensional compact gauge group is the explicit realization of the topological excitation spectrum of T64 high-dimensional self-referential closed chains projected onto a four-dimensional manifold; the non-zero mass gap Delta > 0 represents a rigid constraint imposed by the True-Circle Self-Consistency (TCSC) Law on high-dimensional closed-chain topological excitations, its value uniquely determined by the topological charge of the closed chain and the steady state of self-referential mind-field iteration. This paper completes a six-dimensional refined scheme:1. Holographic embedding of BPST instantons into T64 high-dimensional closed chains.2. Homotopy classification of the instanton moduli space via T64 homotopy groups.3. Proof by contradiction for the positivity of the mass gap Delta > 0 via TCSC fixed-point uniqueness.4. Derivation of an explicit purely topological expression for the mass gap Delta = (2 * pi / alpha) * (Lambda_QCD / l_P) * I(T64).5. Elucidation of the topological mechanisms underlying QCD infrared confinement (string tension area law) and ultraviolet asymptotic freedom (beta function from T64 curvature).6. A complete Lean 4 formal verification framework for machine auditing. Ultimately, this work proves that the mass gap is an inevitable four-dimensional projection of the T64 topological structure, thoroughly resolving the central controversy surrounding this millennium problem. 杨-米尔斯存在性与质量间隙是克雷数学研究所千禧年七大难题之一。本文基于元宪 T64 高维拓扑理论,对该难题完成系统性构造性证明。核心立论:四维紧致规范群杨-米尔斯量子场论是 T64 高维自指闭链在四维投影流形上的拓扑激发谱显式实现;非零质量间隙 Delta > 0 是真圆自洽律(TCSC)对高维闭链拓扑激发的刚性约束,其数值由闭链拓扑荷与自指心场迭代稳态唯一确定。 本文完成了以下六维细化方案:1. BPST 瞬子在 T64 高维闭链中的全息嵌入。2. 基于 T64 同伦群的多瞬子模空间同伦分类。3. 利用 TCSC 不动点唯一性对质量间隙正性(Delta > 0)的严密归谬证明。4. 质量间隙纯拓扑显式表达式推导:Delta = (2 * pi / alpha) * (Lambda_QCD / l_P) * I(T64)。5. QCD 红外禁闭(弦张力面积律)与紫外渐近自由(基于 T64 曲率的 beta 函数)的拓扑机制展开。6. 可供机器审计与复现的完整 Lean 4 形式化验证框架。 最终证明质量间隙是 T64 拓扑结构的四维必然投影,彻底解决了该千禧难题的核心争议。