Navier-Stokes Regularity as a Spectral Problem

We present a spectral-duality analysis of Navier-Stokes regularity. The viscous term −2νH_σ provides decorrelation at rate proportional to viscosity: δ_visc = ν > 0. The grade-3 advective term b_σ(u,u,u) provides δ_adv = 0 in 2D (enstrophy conservation) but δ_adv ≥ 0 in 3D (vortex stretching). We prove that 2D regularity follows from δ_visc > δ_adv = 0, and characterize the 3D obstruction as the question of whether δ_adv can exceed δ_visc.

The enstrophy bound ∫H dt ≤ E₀/(2ν) yields almost-everywhere regularity with δ ≈ 0.5—insufficient for full regularity (δ = 1.0). We identify this as the same L²→L^p barrier that appears in the Riemann Hypothesis (density-1 vs. RH).

We analyze two proof circuits: the Gevrey-Foias-Temam completing-the-square and the grade recursion from the Latent framework. Both are conditional (requiring specific bounds), but their composition formula δ_combined = δ₁ + δ₂ − δ₁δ₂ suggests that even partial results (δ = 0.6 each) combine to significant progress (δ ≥ 0.84).

All 39 theorems are formalized in Lean 4 and verified by the Platonic kernel.

Keywords: Navier-Stokes regularity, spectral methods, decorrelation, Gevrey spaces, formal verification

MSC 2020: 35Q30, 76D03, 76D05