Higher-rank Landau–Ginzburg gluing conjecture for simple normal-crossings pairs

Let $X$ be a quasi-Fano variety with a simple normal crossings anticanonical divisor $D$, and suppose that $X$ admits a semi-stable degeneration into $X_1\cup_{D_0}X_2$. The mirror of $(X,D)$ is a rank $n$ Landau–Ginzburg model, while the mirrors of the two components with their corresponding simple normal crossing divisors are rank $(n+1)$ Landau–Ginzburg models. Higher-rank gluing conjecture for simple normal-crossings pairs. The rank $n$ Landau–Ginzburg mirror of $(X,D)$ can be obtained by topologically gluing the two rank $(n+1)$ Landau–Ginzburg models mirror to $X_1$ and $X_2$ with their corresponding simple normal crossing divisors. This generalizes the rank $1$/$2$ gluing proposal to anticanonical divisors with more than two components; no proof or resolution is given.