  We look for the origins of the single equation, which is a peculiar
combination of W-constrains, which provides the non-abelian W-representation
for generalized Kontsevich model (GKM), i.e. is enough to fix the partition
function unambiguously. Namely we compare it with the scalar projection of the
matrix Ward identity. It turns out that, though similar, the two equations do
not coincide, moreover, the latter one is non-polynomial in time-variables.
This discrepancy disappears for the cubic model if partition function is
reduced to depend on odd times (belong to KdV sub-hierarchy of KP), but in
general such reduction is not enough. We consider the failure of such direct
interpretation of the "single equation" as a new kind of anomaly, which should
be explained and eliminated in the future analysis of GKM.
