Unique Virasoro-compatible deformation conjecture for super tau-covers

Let $M$ be a semisimple Frobenius manifold, let its principal hierarchy have tau function $Z_M$, and let $L_m$ be the operators defining the Virasoro symmetries by

$$\frac{\partial Z_M}{\partial s_m}=L_m Z_M,\qquad m\geq -1.$$

A super tau-cover is the super extension of the tau-cover of a principal hierarchy, and a deformation is homogeneous when it preserves the relevant grading. Unique Virasoro-compatible deformation conjecture. There exists a unique homogeneous deformation of the super tau-cover of the principal hierarchy of $M$ possessing Virasoro symmetries induced by the Virasoro symmetries of $Z_M$ above, where $L_m$ is the operator specified in the source. The conjecture generalizes the uniqueness observed for the KdV super tau-cover; existence and uniqueness for arbitrary semisimple Frobenius manifolds are left unresolved in the source.