The arithmetic point-count conjecture for Berglund–Hübsch Calabi–Yau orbifolds

Let $A$ be an $n\times n$ Berglund–Hübsch matrix over $\mathbb F_p$, with $n\ge 3$, and let $G$ be a subgroup of $G_A$ such that $J\in G\cap G^T$. Assume

$$JA^{-T}J^T=1.$$

Let $X_A$ be the hypersurface in the weighted projective space over $\mathbb F_p$ with weights $w_i=m(JA^{-T})_i$, where $m$ is the smallest integer such that each $w_i$ is an integer, cut out by $W_A(x)=0$. Let $Y_{A,G}$ be the orbifold $[X_A/\langle J\rangle]$, and let $Z_{A,G}(\mathbb F_p)$ be any crepant resolution of $Y_{A,G}(\mathbb F_p)$. Arithmetic point-count conjecture. The number of points of $Z_{A,G}(\mathbb F_p)$ is equal to ${\rm ST}_p(A,G)$.

This conjecture predicts that the point count of a crepant resolution of the Berglund–Hübsch orbifold is governed by the corresponding stringy trace. The supplied text does not state whether the conjecture is known or remains open.