The Riemann Hypothesis and Yang–Mills Theory: Shared Operator Methods and Open Bridges

We compare signed operator estimates for the even polar-anchored theta–Weil form and

lattice SU(2). The common method retains exact equality modes, mixed responses and com-

plete tails in the native normalized law.

For the original arithmetic norm M, a directed 676-pivot certificate gives H[f] ≥ −6 ×

10−12M[f]. A buffered cutoff and a heat comparison yield smaller cofinal suppliers for the

same optimized signed defect. Independently, a complete Gaussian comparison at positive

reference depth 2−15 gives M⊥ ≼ 1.000050221868734I. These are full-domain estimates at

positive tolerance. A vanishing bound for the cofinal signed defect remains open.

On the original isotropic Wilson law, a replica slab exchange and radial comparison control

the inverse-force tails under the exact energy-pair covariance weight. Three color contrasts

can be evaluated together. Their subtraction reduces the remaining Y1 pressure estimate

to a strict bound on one conditional exterior variance, at threshold 216V/b2 in the stated

comparison regime. That variance bound remains open.

We retain earlier finite and auxiliary-lattice certificates, failed sufficient comparisons and

finite detector controls. A cross-theory energy-transfer map and a nontrivial continuum Yang–

Mills theory with uniform physical-time decay remain separate obligations.