2 problems

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Haynes–Marklof conjecture on nearest-neighbor gaps in dimension three
Let $g_N(3,2)$ denote the number of distinct nearest-neighbor distances for the three-dimensional Kronecker sequence with the Euclidean metric. Haynes–Marklof conjecture. In dimens…
Conjectureopengeometry-of-numbers kronecker-sequences nearest-neighbor-gapsarXiv posted 2 days ago
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The three-dimensional nine-distance conjecture for Kronecker sequences
Nine-distance conjecture. For every $N\in{\mathbb N}$ ,
Conjectureopendistance-sets kronecker-sequences torus-geometryarXiv posted 2 days ago

Haynes–Marklof conjecture on nearest-neighbor gaps in dimension three