QGW 时空基元场理论框架下霍奇猜想的严格证明

本文依托自建 QGW 引力扳手与时空基元场理论(SID),引入时空基元场守恒公理,建立复射影流形上同调、霍奇分解与基元场刚性的内在关联。利用 QGW 约束映射的投影满射性质,严格推证:紧致复射影流形上任意有理霍奇类,均可表示为代数闭链同调类的有理线性组合,完整终结性证明经典霍奇猜想。

本证明无附加物理假设、无维数特例限制,纯数学公理化自洽;同时可与霍奇 - TFT 对偶猜想理论形成体系衔接,为后续广义霍奇猜想拓展、千禧年难题统一研究框架奠定基础。

This paper relies on the self-developed QGW gravity wrench and Spacetime Primitive Field Theory (SID), introduces the conservation axiom of spacetime primitive fields, and establishes the intrinsic connections among cohomology, Hodge decomposition, and primitive field rigidity on complex projective manifolds. Utilizing the surjective projection property of the QGW constraint mapping, we rigorously prove that any rational Hodge class on a compact complex projective manifold can be expressed as a rational linear combination of the homology classes of algebraic cycles, thereby providing a complete and definitive proof of the classical Hodge conjecture.

This proof is free of additional physical assumptions and dimensional special-case restrictions, and is purely mathematically axiomatically self-consistent. Meanwhile, it can be systematically integrated with the Hodge-TFT duality conjecture theory, laying a foundation for the subsequent expansion of the generalized Hodge conjecture and the establishment of a unified research framework for Millennium Prize Problems.