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 reflections of the Weyl vectors of the E8 Lie Group. version update for latex error fixes/ Edits to come for redudancy on meromorphic continuation and heat kernel trace, cleaning up 'pillars' etc. some minor citation, and maintaining consistent hat fashion among the operators, and likely breaking the paper into multiple papers for readability. **Cohomology update to come on Ext classes, Left Kan extension of cube faces, various correspondences demonstrated**