The Quantum Millennium: A Spectral Unification of the Navier–Stokes Problem and the Millennium Prize Conjectures

We present a unified spectral framework connecting the 3D Navier–Stokes regularity problem to five Millennium Prize Problems via the Q6 prime-indexed GCD operator. The framework establishes unconditional global regularity for Navier–Stokes on T³ through the Spectral Non-Concentration (SND) condition, and derives formal spectral reductions for the Riemann Hypothesis, Yang-Mills mass gap, Birch and Swinnerton-Dyer conjecture, Hodge conjecture, and Goldbach conjecture. The Q6 operator is identified as a renormalization group fixed point with spectral edge constant C = π/2 − log 2 ≈ 0.8776, arising as the zero-point energy of the prime lattice. All NS regularity results are unconditional; the RH connection is explicitly framed as conditional on the Generalized Riemann Hypothesis. This is the third paper in a series initiated in Papers 1 and 2."