Hodge mapping universality conjecture for the abstract local RH hierarchy

Consider the abstract local RH hierarchy and its hamiltonian perturbations possessing a $\tau$-structure; the abstract local Hodge mapping hierarchy is the hierarchy constructed from the Hodge CohFT in this setting. Hodge mapping universality conjecture. The abstract local Hodge mapping hierarchy is a universal object for hamiltonian perturbations of the abstract local RH hierarchy possessing a $\tau$-structure. This conjecture is motivated by the Hodge universality conjecture and the classification of such perturbations; the supplied text gives no resolution.