Analytical Compatibility Theorem Navier–Stokes (3D Incompressible) and the Double Infinite Cabinet (Energy–Enstrophy)

This theorem establishes that the Double Infinite Cabinet (Energy–Enstrophy) constitutes an analytically correct reformulation of the Navier–Stokes equations. It preserves the original partial differential equation, the conservation and dissipation identities, and makes explicit the intrinsic scale structure and envelope dynamics. The core of the regularity problem is thereby isolated in the control of the enstrophy production term S_k(t) in competition with the viscous dissipation term 2^{2k} Ω_k(t).