Kasprzyk–Tveiten's mirror conjecture for Fano varieties

Let a rigid maximally mutable Laurent polynomial be a Laurent polynomial with the rigidity and maximal-mutation properties used in the source, and identify Laurent polynomials up to mutation. Kasprzyk–Tveiten's mirror conjecture. Fano varieties up to deformation should correspond to rigid maximally mutable Laurent polynomials up to mutation. The conjecture is part of a mirror-symmetry programme for classifying Fano varieties; the source says it has been verified in dimension $2$ and that mirrors have been found for all three-dimensional Fano varieties, while the general correspondence remains open.