A strict gap in the noisy-GHZ equality question of Xu et al., Section 4.2, page 12 of arXiv:2211.05563v1

The question in Xu et al., Section 4.2, page 12 of arXiv:2211.05563v1, asks whether the optimized witness bound equals the convex-roof geometric measure of genuine multipartite entanglement for noisy GHZ states. A strict separation holds for every party count n >= 3 and local dimension d >= 3 at an explicit noise probability. For three qutrits at noise p=3/8, the optimized witness bound is exactly 1/9, whereas the convex roof is at least 13/108. A biseparable overlap inequality and a positive-definite matrix give a two-observable lower bound. A written corollary extends the three-qutrit strict gap throughout 27/74 < p < 9/22.