  In this paper, we formulate and present ample evidence towards the conjecture
that the partition function (i.e. the exponential of the generating series of
intersection numbers with monomials in psi classes) of the Pixton class on the
moduli space of stable curves is the topological tau function of the
noncommutative KdV hierarchy, which we introduced in a previous work. The
specialization of this conjecture to the top degree part of Pixton's class
states that the partition function of the double ramification cycle is the tau
function of the dispersionless limit of this hierarchy. In fact, we prove that
this conjecture follows from the Double Ramification/Dubrovin--Zhang
equivalence conjecture. We also provide several independent computational
checks in support of it.
