Spectral Trace Structure of Confining Yang–Mills Theory A Hilbert–Pólya Framework from Stress–Energy Trace Correlators

A self-adjoint spectral operator associated with the stress–energy trace sector of four-dimensional confining Yang–Mills theory. Using spectral positivity, confinement, and the Yang–Mills trace anomaly, we derive a trace formula consisting of a smooth Weyl term with logarithmic corrections and a discrete oscillatory contribution arising from non- perturbative saddle classes. The associated spectral counting function is shown to obey a logarithmically modified asymptotic growth law. No arithmetic structure is assumed, and no claim is made regarding a proof of the Riemann Hypothesis. We demonstrate, however, that any correspondence between the oscillatory term of the Yang–Mills trace formula and the explicit formula for the Riemann zeta function would necessarily satisfy the Hilbert–Pólya criterion, thereby enforcing the critical-line condition.