Derived equivalence conjecture for mirror Calabi–Yau complete intersections

Let $\{\Delta_1',\ldots,\Delta_r'\}$ and $\{\Delta_1”,\ldots,\Delta_r”\}$ be the translated nef-partitions described in the preceding discussion, with corresponding mirror Calabi–Yau complete intersections $\overline{X}_{\nabla_i'}$ and $\overline{X}_{\nabla_i”}$. Derived equivalence conjecture. There exists an equivalence of Fourier–Mukai type

$$D^b\operatorname{Coh}(\overline{X}_{\nabla_i'})\simeq D^b\operatorname{Coh}(\overline{X}_{\nabla_i”}).$$

The conjecture is motivated by homological mirror symmetry: the two mirror complete intersections have the same stringy Hodge numbers even though no natural isomorphism is available and birational isomorphism may fail. The source supplies no resolution of the proposed derived equivalence.