Maurer–Cartan deformation conjecture for symplectic cochains

Assume $\Bbbk$ has characteristic zero and Hypothesis

holds. Let $(SC^*_{\Lambda},\ell^k)$ be the $L_\infty$ algebra obtained from the symplectic cochain complex, and let $\ell^1_\beta$ denote the differential deformed by a Maurer–Cartan element $\beta\in SC^2_{\Lambda}$. **Maurer–Cartan conjecture.** There \exists a Maurer–Cartan element $\beta\in SC^2_{\Lambda}$ such that the complex in Theorem

can be taken to be $\widetilde{SC}_{\Lambda}=SC_{\Lambda}$ with differential $\partial=\ell^1_\beta$. This would eliminate the replacement of the symplectic cochain complex used in the proof of the deformation theorem, at the cost of a more elaborate $L_\infty$ construction; it remains open.