Route A Reduction for 3D Navier–Stokes Regularity: A Normal-Form Approach

This paper presents a structural reduction of the three–dimensional Navier–Stokes regularity problem to a single geometric–parabolic rigidity scenario. Working at the level of suitable weak solutions, we introduce a normal-form framework that unifies all classical critical obstructions to regularity, including Beale–Kato–Majda blow-up, Littlewood–Paley cascade, Hardy/Lorentz critical tail persistence, halo divergence, and multiscale geometric concentration. The reduction is formalized as a directed implication graph (E1–E6) with explicit quantifiers and closed analytic arrows. All nontrivial analytic input is isolated in a quantitative unique continuation interface, imported only through two black-box theorems: a fixed-time doubling bound and a coefficient-dependent good-time measure estimate. The main result shows that finite-time singularity can occur only if vorticity exhibits persistent two-sided annular concentration across arbitrarily many dyadic scales, leading to exponential lower doubling that contradicts the quantitative unique continuation upper bounds on good times. Regularity is therefore reduced to the exclusion of a single quantified geometric amplification scenario. The paper establishes a complete structural classification of all possible blow-up geometries compatible with scale-critical Navier–Stokes dynamics and isolates the problem of regularity to a single geometric–parabolic rigidity conjecture.