NiO negative-control test structure for the magnetic-ordering gate: 4-atom cell (2 Ni + 2 O) with the two Ni sublattices made inequivalent by a ±0.04 Å displacement along [111] (rhombohedral-type distortion, as in real AFM-II NiO below T_N), with seeded AFM moments of ±2 μB in magCIF moment tags. Purpose: test whether the Magnetic moments DFT route can resolve AFM order when both magnetic sublattices survive primitive reduction and AFM moments are seeded.