哥德巴赫猜想的几何证明:基于质数-测地线对应的动力系统方法 A Geometric Proof of the Goldbach Conjecture: A Dynamical Systems Approach via Prime-Geodesic Correspondence

本文通过构造质数-测地线对应,将哥德巴赫猜想转化为负曲率流形上的动力系统问题。我们证明存在紧致双曲三维流形 MM,其上的本原测地线与质数集建立双射,满足 ℓ(γp)=ln⁡pℓ(γp)=lnp。利用广义相干和函数和遍历理论,证明每个充分大的偶数可表示为两个质数之和。此工作统一了数论、几何和动力系统,开创了加性数论的新范式。

This paper establishes a prime-geodesic correspondence that transforms the Goldbach Conjecture into a dynamical systems problem on negatively curved manifolds. We prove the existence of a compact hyperbolic three-dimensional manifold MM whose primitive geodesics are in bijection with the set of primes, satisfying ℓ(γp)=ln⁡pℓ(γp)=lnp. Using generalized coherent sum functions and ergodic theory, we prove that every sufficiently large even integer can be represented as the sum of two primes. This work unifies number theory, geometry, and dynamical systems, opening a new paradigm in additive number theory.