3 problems

Higher-dimensional Terminal Lemma. For all sufficiently large $d\in\mathbb{N}$, if the Shokurov minimal log-discrepancy is at least

Vasyunin's conjecture. Up to a permutation of the coordinates in $T^{(2d+1)}$, the corresponding points lie in the subtorus

Vasyunin's completeness conjecture. Vasyunin's lists for $d=3$ and $d=4$ are complete.