The open mirror map conjecture for semi-Fano toric manifolds

Let $X$ be a semi-Fano toric manifold, and let $m$ denote the number of its toric divisors. For $i=1,\ldots,m$, let $\delta_i(q)$ be the generating-function correction determined by open Gromov–Witten invariants, let $g_0^{(i)}(\check{q})$ be the corresponding function in the toric mirror map, and let $\check{q}=\check{q}(q)$ be the toric mirror map. Open mirror map conjecture. For $i=1,\ldots,m$, the generating function $1+\delta_i(q)$ and $g_0^{(i)}(\check{q})$ satisfy

$$1+\delta_i(q)=\exp\left(g_0^{(i)}(\check{q})\right)$$

under the toric mirror map $\check{q}=\check{q}(q)$. This conjecture identifies the generating functions of open Gromov–Witten invariants with the exponential corrections appearing in the mirror map. Together with the stated relation between Seidel and Batyrev elements, it would connect open Gromov–Witten invariants to Seidel representations; no resolution is given in the supplied context.