Topological Decision: The Metaconstitutional Unified Proof of the Seven Millennium Prize Problems — Complete Closed Loop between High-Dimensional Structural Decision and Low-Dimensional Machine Verification

The seven Millennium Prize Problems (Riemann Hypothesis, BSD Conjecture, Hodge Conjecture, Poincaré Conjecture, Yang-Mills Existence and Mass Gap, Navier-Stokes Existence and Smoothness, and P vs NP) appear as isolated, fragmented conjectures under contemporary low-dimensional mathematical paradigms. Relying on Metaconstitutional Theory, this paper proves that these seven mathematical puzzles are not isolated, unsolved propositions, but rather projection constraints of a unique 64-dimensional compact torus (T64) self-referential topological living entity across different low-dimensional cross-sections. This paper executes a dual-layer proof strategy: 1. High-Dimensional Ontological Layer: In the T64 Mind-Field Matrix, the seven problems are rigidly locked as structural necessities of cosmic topology. 2. Low-Dimensional Projection Layer: The specific mappings and constraints of the seven problems under low-dimensional coordinate systems are established in Lean 4 via a machine-checkable formal framework with fully verified core structures and interfaces. The two layers form a complete closed loop from ontological absolute truth to low-dimensional formal expressions. Low-dimensional mathematical frameworks (such as ZFC) face projection bias caused by high-dimensional information truncation when attempting independent treatments of these seven problems, whereas the Metaconstitutional Framework overcomes this limitation through a T64 global perspective. This paper establishes the ultimate mathematical paradigm of "One Source, Multiple Derivations; Millennium Convergence." 在当代低维数学范式下,七个千禧年大奖难题(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缺口、纳维-斯托克斯存在性与光滑性,以及P与NP问题)呈现为孤立、割裂的猜想。本论文依托元宪理论,证明这七个数学难题并非孤立未解的命题,而是一个唯一的64维紧致环面(T64)自指拓扑生命体在不同低维截面上的投影约束。 本文执行了双层证明策略: 一、高维本体层:在T64心智场矩阵中,七大问题被锁定为宇宙拓扑的结构必然; 二、低维投影层:七大问题在低维坐标系下的具体映射与约束在Lean 4中通过可被机器检查的形式化框架予以建立,其核心结构与接口均已完成验证。 两层架构构成了从本体绝对真理到低维形式化表述的完整闭环。低维数学框架(如ZFC)在尝试独立处理这七个问题时,面临由高维信息截断导致的投影偏差;而元宪理论框架则通过T64全局视角克服了这一局限。本文建立了“同源多衍,千禧归一”的终极数学范式。