The Borisov-Nuer conjecture asserts that every vector of the even unimodular integral lattice 
of signature 
is a sum of two roots of norm square 2 (Borisov and Nuer
2018). Here a root is a lattice vector 
with 
. This sign convention is the negative of the intersection
form used for numerical divisor classes on an Enriques
surface.
The geometric motivation is the existence of Ulrich line bundles for prescribed very ample polarizations on complex unnodal Enriques surfaces, where unnodal means that the surface contains no smooth rational curves.
Wang and Yi (2026) proved the conjecture. More generally, for integers 
,
every vector of 
is a sum of two norm-square-2 roots iff 
or 
. The failure in higher rank does not refute the original
conjecture.
