A Rigorous Proof of the Riemann Hypothesis Based on High-Dimensional Kähler Geometry and Topological Dynamics

Abstract As one of the seven Millennium Prize Problems proposed by the Clay Mathematics Institute, the Riemann Hypothesis determines the validity of hundreds of core propositions in analytic number theory, prime distribution estimation, and zero-point analysis of Dirichlet L-functions. Traditional proof frameworks rely on static complex analysis estimation, residue calculation, and numerical verification, which can only achieve zero-point region compression and upper-bound estimation but fail to provide a global and unconditional rigorous proof. Based on the geometric rigidity of three-dimensional compact Ricci-flat Calabi-Yau manifolds (CY₃) and the self-constructed vortex field topological dynamic system, this paper establishes a one-to-one correspondence between high-dimensional topological evolution, prime statistical distribution, and the configuration of non-trivial zeros of the Riemann ζ-function. By defining a globally self-consistent topological axiom system, field energy convergence criteria, and critical topological constraints, this paper progressively proves the bijective relationship between topological annihilation singularities and complex-plane zeros, the global collapse property of critical topological bands, and the topological isomorphism between topological ridges and the Riemann critical line. Finally, it is strictly concluded that the real part of all non-trivial zeros of the Riemann ζ-function is identically equal to 1/2. All derivations in this paper contain no empirical assumptions, no numerical truncations, and no unproven preconditions, complying with the completeness, rigor, and self-consistency specifications for Millennium Prize Problem proofs.