Exact Commutation of the He-Tu Antipodal Projection with Littlewood-Paley Projections (v2): Resolved and Open Steps Toward NS Global Regularity

Update (v2) of Kao2026 Commutator Theorem [DOI:10.5281/zenodo.19906520]. Two findings: (1) RESOLVED: The continuum [Delta_j, R]=0 holds directly by Fourier parity — the same argument as on the lattice, requiring no limit step. Verified numerically to machine precision at N=128,512,2048,8192. (2) NEWLY IDENTIFIED GAP: The He-Tu antipodal constraint omega(x)+omega(x')=B is NOT preserved by NS evolution. Numerical simulation shows antipodal violation grows as O(1) from the first timestep. Therefore the Multiscale Ceiling Theorem and global H^s bound, while correct within the P-projected system, do not directly apply to the original NS equations. The true open problem is identified: does NS evolution preserve any version of the He-Tu antipodal symmetry? This is a question about invariant manifolds and the symmetry structure of NS, not a technical detail. Complete status table provided. No claim is made to resolve the Millennium Prize Problem.