Toward a Proof of the Riemann Hypothesis via Phase–Curvature Dynamics

Abstract After centuries of purely analytic pursuit, the Riemann Hypothesis is reframed within a geometric and dynamical context. Through the Phase–Curvature Framework, the zeta function is promoted from a static analytic object to a self-organizing phase field governed by a geometric wave equation. This manifesto summarizes the current stage: the critical line as an equilibrium of a positive-curvature analytic field, zeros as quantized vortices, and the remaining frontier—a formal positivity proof—as the final step toward closure.