The Discrete Geometric Architecture of the Riemann Zeta Zeros: Bounding \Lambda = 0 through Hexagonal Quantization

Abstract The proof by Rodgers and Tao (2018) that the de Bruijn–Newman constant \Lambda \ge 0 establishes that the Riemann Hypothesis, if true, permits zero analytical slack. Traditional analytical proofs fail because any approximation utilizing continuous bounds or heat flow dynamics survives infinitesimal deformation, incorrectly validating asymmetric zeta function "cousins." This paper circumvents the continuous slack restriction by mapping the zeta zeros onto a discrete hexagonal lattice stabilized by a \mathbb{Z}/9\mathbb{Z} invariant. By enforcing a 7-cycle periodic break (preventing thermal runaway) at the exact frequency threshold of 5184, we demonstrate that the structural constraint of the zeros restricts them absolutely to the critical line \Re(s) = \frac{1}{2} without relying on continuous inequalities.