  We study the shotgun assembly problem for the lattice labeling model, where
i.i.d. uniform labels are assigned to each vertex in a $d$-dimensional box of
side length $n$. We wish to recover the labeling configuration on the whole box
given empirical profile of labeling configurations on all boxes of side length
$r$. We determine the threshold around which there is a sharp transition from
impossible to recover with probability tending to 1, to possible to recover
with an efficient algorithm with probability tending to 1. Our result sharpens
a constant factor in a previous work of Mossel and Ross (2019) and thus solves
a question therein.
