Spectral Unification of the Riemann Hypothesis, Yang–Mills Mass Gap, P vs NP and Navier–Stokes Regularity in the qdRIS Framework

We present an explicit spectral construction in the qdRIS framework that unifies fourMillennium Problems: the Riemann Hypothesis, the Yang–Mills mass gap, P vs NP, andthe Navier–Stokes regularity problem. A single operator Q2 on a separable Hilbert spaceHh0 is shown to control all four:• RH ⇐⇒ spectral symmetry of Q2,• YMgap ⇐⇒ spectral coercivity of Q2,• Pvs NP ⇐⇒ spectral traversability,• NS regularity ⇐⇒ spectral boundedness.All conditions are equivalent to the existence of a finite resolution h0 > 0, which is fixedby geometry (electroweak scale, black hole thermodynamics). The construction includesan explicit Hilbert–Pólya type potential, a strong trace formula, and a derivation of theprime amplitudes logppk/2 from spectral dynamics. This is not a solution to the problems intheir classical formulation (h0 = 0), but a demonstration that they become equivalent andstructurally resolved under finite resolution. Future work may extend this unification to theHodge conjecture and the Birch–Swinnerton-Dyer conjecture, using the spectral operatorformalism developed in the companion articles