A Kinematic–Geometric Criterion for Zeros of the Riemann Zeta Function

We introduce a geometric stabilization framework for the Dirichlet partial sums on the critical line, based on a phase-locking mechanism that forces the walk into a non-degenerate square-root helical regime. We prove a one-directional implication: whenever this helical locking occurs, the de-trivialized remainder cancels and a zero of the Riemann zeta function is produced on the critical line. The construction establishes a structural identity between the helical regime and the log-frequency resonance modes of the integer system. Within this framework, zeros appear not as isolated analytic accidents, but as stable resonance states of the Dirichlet walk. Extensive numerical experiments demonstrate a sharp statistical separation between the helical signature at true zeros and generic off-zero points. While the formal proof is one-directional, the results suggest that the helical mechanism captures the entire spectral class of "meaningful" zeros---those encoding the arithmetic structure of prime oscillations.