This preprint is the second module of a modular TEBAC-based program toward the three-dimensional incompressible Navier--Stokes existence and smoothness problem. It continues the foundational Stokes--Galerkin--spectral-cascade framework developed in the preceding NS-I module and focuses on the next structural layer: the conversion of the large-data cascade residue into a precise vorticity-to-shell and resonance-classification ledger. The manuscript works on the periodic domain \ (T³\). It records the vorticity equation, the enstrophy identity, the vortex-stretching production term, dyadic vorticity-shell balances, transport commutator residues, low--high / high--low / high--high interaction classes, Fourier triadic enstrophy-production formulae, geometric depletion mechanisms, and the first TEBAC resonance-classification framework. The main role of NS-II is not to claim a complete solution of the Navier--Stokes Millennium problem. Rather, it closes the second module as a decomposition and classification module. It translates the large-data obstruction isolated in NS-I into the critical resonance-absorption target exported to NS-III. The decisive exported target is a TEBAC critical resonance absorption estimate of the form \Q^crit (uN;t) ₐ>ₐ\|N^ (q) (t) \|₋ℂ^2+ R₋₎ₖ (uN;t), 0<<1, \ where \ (Q^crit\) denotes the critical high-frequency resonance contribution and \ (R₋₎ₖ\) is a lower-order residue to be controlled by previously available energy/enstrophy ledgers. Thus NS-II is closed as a vorticity-to-shell decomposition and resonance-classification module, while the full arbitrary-data no-cascade theorem is deliberately reserved for the subsequent NS-III module.
Tosho Lazarov Karadzhov (Tue,) studied this question.