Kontsevich's Fukaya-category reconstruction conjecture for Gromov–Witten invariants

Let $X$ be a symplectic manifold, let $\mathcal{F}uk(X)$ denote its Fukaya category, and let the Gromov–Witten invariants of $X$ be its symplectic enumerative invariants. Kontsevich's Fukaya-category reconstruction conjecture. The Fukaya category determines the Gromov–Witten invariants of the symplectic manifold. Genus-zero cases for Calabi–Yau varieties are reported under suitable assumptions, but the arbitrary-genus statement remains open; it is the target to which the paper's open-closed field-theoretic construction is intended to contribute.