An octahedron covering is a covering of three-dimensional Euclidean space by translates of an octahedron. For a convex
body 
and a full-rank point lattice 
, the lattice covering density is the volume
of 
divided by the volume of a fundamental
parallelepiped of 
, provided the translates 
cover space.
Lian and Xue (2026) proved
 |
where 
is the regular octahedron and 
denotes its lattice covering density, settling the
conjectured value. The authors report using ChatGPT to check details of the argument,
improve the exposition, and prepare the manuscript, while retaining full responsibility
for the mathematical claims.
