Gross–Pavanelli mirror-symmetry conjecture for quotients of V_{8,w}^{1}

Let $V_{8,w}^{1}$ be the Calabi–Yau threefold fibered by $(1,8)$-polarized abelian surfaces, with a free action of $\mathbb{Z}_{8}\times\mathbb{Z}_{8}$, and let $\mathbb{Z}_{8}\subset\mathbb{Z}_{8}\times\mathbb{Z}_{8}$ be a subgroup. Gross–Pavanelli conjecture. The mirror of $V_{8,w}^{1}$ is $V_{8,w}^{1}/\mathbb{Z}_{8}$, while the mirror of $V_{8,w}^{1}/\mathbb{Z}_{8}$ is $V_{8,w}^{1}/(\mathbb{Z}_{8}\times\mathbb{Z}_{8})$. This conjecture is motivated by the common Hodge numbers and the expected mirror relationships among these three Calabi–Yau manifolds; the stated version was partly confirmed by derived equivalence between $V_{8,w}^{1}$ and $V_{8,w}^{1}/(\mathbb{Z}_{8}\times\mathbb{Z}_{8})$, but the full mirror correspondence remains unresolved.