  In the recent study of Virasoro action on characters, we discovered that it
gets especially simple for peculiar linear combinations of the Virasoro
operators: particular harmonics of $\hat w$-operators. In this letter, we
demonstrate that even more is true: a {\it single} $w$-constraint is sufficient
to uniquely specify the partition functions provided one assumes that it is a
power series in time-variables. This substitutes the previous specifications in
terms of {\it two} requirements: either a string equation imposed on the
KP/Toda $\tau$-function or a pair of Virasoro generators. This mysterious {\it
single}-entry definition holds for a variety of theories, including Hermitian
and complex matrix models, and also matrix models with external matrix: the
unitary and cubic Kontsevich models. In these cases, it is equivalent to
W-representation and is closely related to {\it super}\,integrability. However,
a similar single equation that completely determines the partition function
exists also in the case of the generalized Kontsevich model (GKM) with the
potential of higher degree, when the constraint algebra is a larger
$W$-algebra, and neither W-representation nor superintegrability are understood
well enough.
