  In 2020, a paper [arXiv:2010.13443] appeared in the arXiv claiming to prove
that a Moore graph of diameter 2 and degree 57 does not exist. (The paper is in
Russian; we include a link to a translation of this paper kindly provided to us
by Konstantin Selivanov.) The proof technique is reasonable. It employs the
fact that such a graph must be distance regular and that there exists a large
set of relations which such a graph must satisfy. The argument proceeds by a
case analysis that shows that this set of relations cannot be satisfied. We
show that this seems not to be correct. The system of equations factors into
small diagonal blocks all of which have solutions. As an alternative, we show
that there is a family of systems of permutations with the property that the
Moore graph exists if and only if there is a member of the family with no
solutions.
