The normal-crossing-divisor generalization conjecture for Lagrangian Floer theory

Let $(X,\omega)$ be a compact symplectic manifold, let $\mathcal D=\bigcup_{i=1}^m\mathcal D_i$ be a normal crossing divisor, and let $L\subset X\setminus\mathcal D$ be a compact relatively spin Lagrangian. Consider homology classes $\beta\in H_2(X,L;{\mathbb Z})$ satisfying $\beta\cap[\mathcal D_i]=0$ for every $i$. Normal-crossing-divisor generalization conjecture. Theorem and Conjectures and can be generalized to this setup. The proposed generalization is expected to use RGW-type compactifications and Kuranishi structures for the corresponding moduli spaces; the source does not prove it.