We present a geometric framework for the Riemann zeta function by analyzing Dirichlet partial sums, S_n(s), as vector walks in the complex plane. We identify a fundamental stability regime, termed the "perfect helix", which serves as the unique rigid asymptotic configuration compatible with the kinematic stabilization of the walk. Our analysis proceeds in two stages: (i) We prove that the emergence of this helical regime is critical-line selective, as any deviation Re(s) != 1/2 introduces a radial drift that precludes such stability. (ii) We employ the perfect helix as an analytic probe to decompose the remainder term of the zeta function. Using an Euler-Maclaurin expansion, we demonstrate that the resulting second-stage residual possesses a non-vanishing leading term of order n^-sigma. Due to the asymptotic decoupling between the helical carrier and this residual, the vanishing of the zeta function is shown to be forced exclusively by the exact helical cancellation mechanism. This geometric rigidity implies that all non-trivial zeros are confined to the critical line, providing a structural basis for the Riemann Hypothesis. Numerical evidence from the first 10,000 zeros confirms the systematic onset of this stabilized helical geometry.