From Hilbert-Pólya to Yang-Mills: Realizing the Riemann Hypothesis and the Mass Gap.

Proof of Riemann's Hypothesis, the Birch Swinnerton-Dyer Conjecture, and the Yang Mills Mass Gap using the Hilbert-Polya operator and Weyl root geometry. Indentifying these functions as eigenfunctions of Weyl roots as or reflections of the Weyl vectors of the E8 Lie Group. Edits to come for redudancy, some minor citation, and maintaining consistent hat style among the operators, and likely breaking the paper into multiple papers for readability.