Topological deformation conjecture for Virasoro actions

Consider a deformation of the bihamiltonian structure of the Principal Hierarchy, and let its central invariants be the functions parametrizing the infinitesimal deformation. The associated deformation of the Virasoro symmetries acts on the tau function of the deformed integrable hierarchy. Topological deformation conjecture. When the central invariants of the deformation of the bihamiltonian structure of the Principal Hierarchy are all equal to $\frac{1}{24}$, the corresponding deformation of Virasoro symmetries can be represented by linear actions on the tau function. This is the distinguished topological deformation among deformations with constant central invariants; the source does not state a resolution of this conjecture in the present paper.