Buryak's DR/DZ equivalence conjecture

Let a semisimple CohFT be given, and let its associated Dubrovin–Zhang (DZ) and double ramification (DR) hierarchies be the corresponding tau-symmetric integrable hierarchies. Buryak's conjecture. Given a semisimple CohFT, the associated DZ and DR hierarchy coincide up to a Miura transformation. The conjecture is motivated by the agreement for the trivial CohFT and by the identification of the DR hierarchy with the intermediate long wave hierarchy for the Hodge CohFT. The stronger normal-Miura formulation below is presented as a refinement.