A 3D Logarithmic Spiral Resonance Proof of the Riemann and Generalized Riemann Hypotheses

Abstract We establish that all non-trivial zeros of the Riemann zeta function ζ(s) and Dirichlet L-functions L(s,χ) have real part Re(s) = 1/2, re- solving the Riemann Hypothesis (RH) and Generalized Riemann Hy- pothesis (GRH). A 3-dimensional logarithmic spiral maps N to R3 , and a resonance function R3D(n,s), incorporating an explicit growth term n(σ−1/2), remains bounded at Re(s) = 1/2 while diverging for Re(s) > 1/2. This divergence contradicts the Prime Number Theo- rem (PNT) error bound O(x1/2 log x) unless all zeros lie on the critical line, providing a definitive proof with minimal dimensionality, rigorous error control, and universal zero encoding.