Universality of the Hodge hierarchy for deformations of the Riemann hierarchy

Let a tau-symmetric integrable Hamiltonian deformation of the Riemann hierarchy be given by a hierarchy of scalar Hamiltonian evolutionary PDEs with Hamiltonian densities and Hamiltonian operator of the stated homogeneous form, satisfying the tau-symmetry conditions for the one-dimensional Frobenius manifold. A normal Miura-type transformation is an equivalence transformation in this class. Universality conjecture. Any nontrivial tau-symmetric integrable Hamiltonian deformation of the Riemann hierarchy is equivalent, under a normal Miura-type transformation, to the Hodge hierarchy of a point with a particular choice of the parameters $s_k$, $k\geq 1$. The conjecture proposes a universal normal form for this class of deformations; the source gives no resolution, so its general status remains open.