The relative wrapped Fukaya category completion conjecture

Let $X\to Y$ be a rank-one algebraic torus fibration with discriminant divisor $D\subset Y$, and let $s$ denote the invertible variable associated with the $S^1$ action on $X$. Let $\mathcal{W}(Y,D)$ be the relative wrapped Fukaya category, defined over $\mathbb{C}[[h]]$. Relative completion conjecture. The relative wrapped Fukaya category is equivalent to the completion of $\mathcal{W}(X)$ at $s=-1$:

$$\mathcal{W}(Y,D)\simeq\widehat{\mathcal{W}(X)}_{s=-1}.$$

The claim compares the relative category, whose central fibre is related to $\mathcal{W}(Y\setminus D)$ and whose generic fibre recovers $\mathcal{W}(Y)$, with the formal completion of the total-space category at the singular spectral value.