Conjecture on the extended constrained KP hierarchy

Consider the constrained KP hierarchy and its extension obtained by adjoining the additional set of flows associated with the logarithm of its Lax operator. Let the associated Frobenius manifold have its principal hierarchy, and let the topological deformation of that principal hierarchy be formed. Extended constrained KP hierarchy conjecture. The extended constrained KP hierarchy coincides with the topological deformation of the principal hierarchy of the associated Frobenius manifold. This conjecture concerns the identification of the extended integrable hierarchy with the Frobenius-manifold hierarchy; the supplied text gives no resolution status.