Domain-dependent neck-stretching Maurer–Cartan conjecture

Let $X$ be a symplectic manifold, let $V\subset X$ be a symplectic crossing divisor carrying the symplectic form, and let $D\subset X\setminus V$. The intrinsic symplectic cochains of $D$ are denoted by $SC^*_{\theta}(D)$. Domain-dependent neck-stretching Maurer–Cartan conjecture. There is a Maurer–Cartan element $x\in SC^*_{\theta}(D)$, well-defined up to gauge equivalence, such that

$$SC^*_M(D)\simeq \text{the twist of }SC^*_{\theta}(D)\text{ by }x.$$

This conjecture is proposed as the outcome of a domain-dependent neck-stretching scheme, providing an alternative to the SFT-type construction of deformation data.