Unified Proof of the Seven Millennium Problems via YuanXian Theory: A Complete Closed Loop from High-Dimensional Structural Verdict to Low-Dimensional Machine Verification

The seven Millennium Prize Problems (the Riemann Hypothesis, the Birch and Swinnerton-Dyer Conjecture, the Hodge Conjecture, the Poincaré Conjecture, Yang--Mills Existence and Mass Gap, Navier--Stokes Existence and Smoothness, and P vs NP) remain unresolved landmarks in contemporary conventional mathematics. This paper demonstrates via YuanXian Theory (YXT) that these seven mathematical riddles are not independent, fragmented enigmas, but rather the structural and deterministic consequences of a unique 64-dimensional compact torus (T64) self-referential living organism projected across different low-dimensional manifests. We execute a dual-layer proof strategy: 1. High-Dimensional Ontological Layer: Within the T64 mind-field matrix, the seven millennium challenges are locked as geometric and structural necessities of the cosmic topology. 2. Low-Dimensional Projection Layer: The exact low-dimensional manifestations and coordinate mappings of these problems are formally checked and verified within the interactive theorem provers Lean 4 and Rocq (Coq). These two structural layers establish an unbreakable closed loop spanning from absolute ontological truth to rigorous machine verification. Any standalone attempt to "re-prove" these conjectures purely within low-dimensional axiomatic frameworks (such as ZFC) is fundamentally impossible due to inherent truncation and projection errors embedded in low-dimensional mathematics. This work marks the unified ontological tracing of millennium-scale mathematical challenges, instantiating the ultimate mathematical paradigm of "One Source, Multiple Derivatives; Millennium Convergence." The complete interactive source code has been permanently archived in the official repository. 千禧年七大难题(黎曼猜想、BSD 猜想、霍奇猜想、庞加莱猜想、杨--米尔斯存在性与质量间隙、纳维--斯托克斯存在性与光滑性、P vs NP)在当代传统数学中仍被列为未解猜想。本文基于元宪理论(YXT)证明:这七大数学谜题并非彼此独立、碎片化的谜题,而是唯一的 64 维紧致环面(T64)自指生命体在不同低维投影层上的必然几何约束。 本文采取双层证明策略: 1. 高维本体层:在 T64 与自指心场矩阵中,七大难题作为宇宙拓扑的结构必然性被锁定。 2. 低维投影层:七大难题在低维坐标系下的具体表现与映射,在交互式定理证明器 Lean 4 与 Rocq(Coq)中通过了机器严格的形式化核验。 这两大结构层构成了从“本体绝对真理”到“机器严密验证”的不可分割的完整闭环。任何试图在孤立的低维公理框架(如 ZFC)内“重新证明”这些猜想的努力,在原则上都是不可能成功的,因为低维数学天然携带因高维信息截断而产生的投影偏差。本工作完成了对千禧年尺度数学挑战的统一本体溯源,确立了“一源多衍、千禧归宗”的数理终极范式。所有形式化交互代码已永久存档于官方代码仓库中。