Fukaya-category matrix-factorization conjecture for a one-critical-value Landau–Ginzburg model

Let $(X,f:X\to\mathbb{C})$ be a Landau–Ginzburg Weinstein sector such that $f$ has no critical values outside $0$, and let $F$ be a general fiber of $f$. Let $\mathcal{W}(X,f)$ and $\mathcal{W}(F)$ denote the corresponding wrapped Fukaya categories, and let $\mathcal{X}^\circ$ denote the very affine part of $X$. The cup functor has a right adjoint cap, and its monad is presented as

$$\operatorname{cap}\operatorname{cup}=\operatorname{Cone}(\mu^{-1}\xrightarrow{s}\operatorname{id}_{\mathcal{W}(F)}).$$

Let $\widetilde{s}\in HH^0(\mathcal{W}(\mathcal{X}^\circ,f|_{\mathcal{X}^\circ}))$ be the Hochschild class induced by $s$. Fukaya-category matrix-factorization conjecture. There is an equivalence

$$\mathcal{W}(X,f)\cong\operatorname{MF}(\mathcal{W}(\mathcal{X}^\circ,f|_{\mathcal{X}^\circ}),\widetilde{s}).$$

This formalizes a procedure for computing the Fukaya–Seidel category of a Landau–Ginzburg model with a single critical value; the source notes that it is expected in general and easy to prove in several cases, but leaves the complete statement as a conjecture.