Vorticity Boundedness in 3D He-Tu Lattice Boltzmann Method: A Direct Consequence of the Non-Expansive Projection Theorem

We demonstrate that the Non-Expansive Projection Theorem (Theorem 4) and the Boundedness Theorem (Theorem 2) established in the Genesis 3D He-Tu Lattice Boltzmann Method (3D-HLBM) directly imply vorticity boundedness for Navier-Stokes flows discretized on the 27-node He-Tu lattice. The antipodal-pair constraint structure of the 3x3x3 He-Tu lattice — comprising 13 antipodal pairs and one fixed center node — enforces ||omega(t)||_inf <= B for all t. Combined with the Beale-Kato-Majda criterion, this yields global-in-time smooth solutions on the He-Tu lattice. The geometric mechanism is identified: antipodal pairing forbids simultaneous vorticity growth at symmetric nodes, preventing finite-time blowup at the lattice level. The relationship to E8 root system geometry and U(3) gauge conservation provides additional structural support for the conjecture that this boundedness survives the continuum limit. The continuum limit claim is explicitly identified as open. No claim is made to resolve the Millennium Prize Problem.