We develop a spectral-fractal approach to the 3D incompressible Navier-Stokes global regularity problem — one of the Clay Millennium Prize Problems — combining four innovations that exploit the fine structure of the nonlinear term, satisfying the Tao supercriticality barrier. The first innovation is the intrinsic emergence of √2 from incompressibility: when a vortex tube stretches by factor λ, incompressibility forces transverse contraction by 1/√λ. For one-octave doubling (λ = 2), the contraction ratio is 1/√2. This is geometry, not assumption — verifiable from ∇·u = 0 alone. The second is a visco-elastic analogy: viscous dissipation acts as a super-Hookean restoring force in the enstrophy cascade, with dissipation dominance scaling as (1/2) ⁿ per cascade level — exponential suppression without any parameter choice. The third is a fractal-temporal reparametrization exploiting the bounded enstrophic time budget from the energy identity: the total time during which enstrophy can be large is unconditionally finite. The fourth is the Kesten-Stigum reconstruction threshold applied to the enstrophy cascade tree, showing that the cascade is in the disordered phase (b·η² ≪ 1) and no coherent enstrophy concentration can survive. What is proved unconditionally: √2 emergence from incompressibility; exponential dissipation dominance (1/2) ⁿ; bounded enstrophic time budget; super-Hookean structure; bootstrap closure conditional on dₑff 1 (unstable — blow-up possible). For NS (ν > 0), Φ_ν' (d*) < 1 (stable — regularity forced). Viscosity is the mechanism, consistent with the Clay problem asking about NS, not Euler. Empirical support: DNS measurements of vorticity fractal dimension D ≈ 1. 3–1. 5 (She et al. 1990, Jiménez et al. 1993), consistent with √2 ≈ 1. 414. Independent contributions (√2 emergence, elastic analogy, enstrophic time budget, NS/Euler distinction) are valuable regardless of whether the full program succeeds.
Thierry Marechal (Sun,) studied this question.