The Metriplectic Attractor of the Riemann Hypothesis

We propose a dynamical framework for the Riemann Hypothesis (RH) based on a “Generator–Filter” duality (Azari, 2025a). By interpreting the prime distribution as a local arithmetic generator (G) and the zeta zeros as a global spectral filter (F), we map the explicit formula onto a metriplectic dynamical system. We utilize a Weil-type energy functional to model the misalignment between these distributions. We demonstrate that under the assumption of Weil positivity, the critical line ℜ(s) = 1/2 corresponds to the unique global attractor of the system—a state of minimal energy dissipation. This formalism reinterprets the Riemann Hypothesis as a condition of dynamical stability.