Conjecture on instanton corrections and the local mirror map

Let $X$ be a smooth variety with a smooth nef anticanonical divisor $D$, and consider the local Calabi–Yau manifold $\mathcal O_X(-D)$. The instanton corrections are the corrections appearing in the mirror construction of this local Calabi–Yau manifold, and the local mirror theorem relates local Gromov–Witten invariants to periods. Instanton-correction conjecture. The instanton corrections of $\mathcal O_X(-D)$ are the inverse mirror map of the local mirror theorem relating local Gromov–Witten invariants with periods. This is presented as the principal open–closed duality expectation beyond the toric setting. The source does not state a resolution, so the conjecture is recorded as open.