Hilbert Space Symmetries and Norm Positivity in Spectral Gap Arguments for Yang--Mills Theory

We present a spectral gap framework for Yang–Mills theory grounded in Hilbert space methodsoriginally developed in a rigorous proof of the Riemann Hypothesis. Specifically, we repurposethe core symmetry and norm positivity arguments from the RH proof to constrain the energyspectrum of the Yang–Mills Hamiltonian defined on compactified time manifolds. By identifying aprecise mapping between the symmetry structure of the ξ-function and the compactified temporalsymmetry in gauge theory, we derive a variational exclusion principle for small eigenvalues. Thismethod uses the RH structure not as an analogy but as an analytical framework, offering a novelroute toward resolving the Yang–Mills mass gap problem.