A Proposed RG–Spectral Framework for the Stability of the Critical Line via Prime Variance Invariance

We present a proposed renormalization-group–spectral framework within ZFC set theory thatformally reduces the Riemann Hypothesis to the stability of the critical line Re(s) = 1/2 under the deBruijn–Newman flow. By differentiating Connes' trace formula along the flow and mapping theresulting operator dynamics through the Weil explicit formula, we identify a structural mechanism inwhich the stability of the critical line is dynamically enforced by the invariant variance of the primedistribution. Under this framework, off-critical energy formally decays exponentially at a rategoverned by a strictly positive constant derived from prime distribution variance. We do not claim aproof of the Riemann Hypothesis. Rather, we present this as a coherent structural proposal andidentify the key analytical challenge that remains open: establishing the L² + entropy ® L¥inequality that would close the argument. This formulation connects analytic number theory,noncommutative geometry, and renormalization-group methods within a single ZFC-consistentframework.