The FOOO obstruction-term conjecture for the open mirror map

Let $Y$ be a symplectic Fano manifold with smooth anticanonical divisor $D$, such that $Y\setminus D$ supports a Lagrangian torus fibration collapsing an $S^1$ along $D$. Let $L$ be a torus fiber near $D$, and let $\delta$ be the disc class of the thimble of the collapsing $S^1$. Let $m_0$ denote Fukaya–Oh–Ohta–Ono's obstruction term of the Lagrangian Floer complex for $L$ with itself. FOOO obstruction-term conjecture. The product

$$\exp\left(\int_\delta\omega\right)\cdot m_0$$

is the open mirror map of $K_Y$. This proposes a symplectic and Floer-theoretic description of the open mirror map in terms of the obstruction term for a torus fiber near the anticanonical divisor; the source gives no resolution of the conjecture.