Eynard–Orantin construction of dispersive universal Whitham tau-functions

Let a spectral curve be the spectral-curve datum to which Eynard–Orantin topological recursion applies, and let the associated dispersive universal Whitham hierarchy be the hierarchy expected to arise from that curve. Eynard–Orantin conjecture. By Eynard-Orantin topological recursion one can construct a tau-function of the dispersive universal Whitham hierarchy associated with the spectral curve. This would provide an emergent construction of tau-functions from spectral curves and connect topological recursion with dispersive integrable hierarchies; the source gives no resolution.