Rigidity and Helical Structure in the Riemann Zeta Function

We present a bidirectional proof framework for the Riemann Hypothesis composed of twoone-sided arguments: a necessity direction and a uniqueness direction. The first direction is geometric. It shows that a non-degenerate helical phase–amplitudelocking of the Dirichlet walk necessarily produces analytic cancellation, and that suchperfect helices can occur only on the critical line Re(s) = 1/2. The second direction is structural and number-theoretic. It interprets a zero as ano-distortion state between a discrete Dirichlet sum and its canonical linear/analyticsurrogate, and proves that in a deterministic setting this discrete–continuous gap admitsa unique intrinsic mediation pattern. Any admissible one-sided zero-witness must thereforeinstantiate the same underlying structure, identified here with the helical mechanism. Extensive numerical experiments on the first 10000 nontrivial zeros exhibit a sharp andexclusive helical signature, providing strong empirical support for the rigidity principleunderlying the argument.