Krichever's dispersive universal Whitham hierarchy conjecture

Let a punctured Riemann surface be a Riemann surface of arbitrary genus equipped with punctures, and let Krichever's construction associate to it a universal Whitham hierarchy. Krichever's conjecture. One can generalize Krichever's construction of the universal Whitham hierarchy on punctured Riemann surfaces of arbitrary genera to the dispersive case. This would extend the universal Whitham construction from the dispersionless setting and strengthen the connection between spectral curves and integrable hierarchies; the source presents it as an open conjecture.