Relative symplectic cohomology and Maurer–Cartan deformation conjecture

Let $M$ be the positively monotone symplectic manifold and $D$ the normal-crossings divisor considered in the paper, let $X=M\setminus D$, and let $\mathbb{L}$ be the skeleton of $X$. Let $R$ be the coefficient ring, $\bk$ the ground field, and $\beta$ the Maurer–Cartan element used to deform symplectic cohomology. Write $SH^*_M(\mathbb{L};R)$ for relative symplectic cohomology.

Relative symplectic cohomology conjecture. There is an isomorphism of graded $R$-modules

$$SH^*_M(\mathbb{L};R) \cong H^*\left(SC^*(X;\bk) \wotimes_\bk R,\ell^1_{\beta}\right).$$

This generalizes the theorem proved under Hypothesis A, namely the condition that all divisor weights satisfy $\lambda_j\leq 2$. It is known in the cases covered by that theorem and is conjectured more generally, including examples where both sides vanish and the case of $M=\mathbb{CP}^1\times\mathbb{CP}^1$ with $D$ a $(1,1)$ hypersurface.