Riemann Hypothesis on the critical line

Prove that all nontrivial zeros of the Riemann zeta function ζ(s) lie on the critical line Re(s) = 1/2 in the complex plane.

Background

The paper investigates chaotic dynamics derived from the Riemann–von Mangoldt formula and proposes a chaotic operator that the authors argue is compatible with the Hilbert–Pólya perspective. They provide numerical observations (e.g., predominantly real eigenvalues from a random matrix model derived from their operator) that they claim support the Riemann Hypothesis.

Within this context, the Riemann Hypothesis is explicitly recalled as the central open conjecture about the location of nontrivial zeros of ζ(s), serving as the primary mathematical target that motivates the construction and analysis of their operator.