A Geometric Framework for the Riemann zeta Function via Dirichlet Helix Dynamics

We present a geometric framework for the nontrivial zeros of the Riemann zeta function based on a geometric analysis of the Dirichlet partial sums. The approach interprets the Dirichlet walk as a geometric dynamicalsystem and studies its stabilized behavior after removal of the universal analytic main term. Within this framework the tail dynamics exhibit a clear geometric dichotomy: either persistent rotation (wave state) or collapse of the rotation (line state). Collapse of the rotation induces a locking mechanism in the Dirichlet walk that stabilizes both phase and amplitude in the sqrt(n)--normalized frame, producing a nondegeneratehelical structure. The geometric framework shows that such stabilized helices can occur only on the critical line Re(s)=1/2, due to geometric stability constraints arising from the combinatorial structure of the zeta Dirichlet walk. This provides a geometric interpretation of the location of the nontrivial zeros of the Riemann zeta function.