The open–closed isomorphism conjecture for Fukaya categories

Let $M$ be an exact symplectic manifold satisfying Assumption, and let

$$SH^*(M) \longrightarrow HH^*(\mathcal F(M),\mathcal F(M))$$

be the natural open–closed string map from symplectic cohomology to the Hochschild cohomology of the Fukaya category. Open–closed isomorphism conjecture. The map is an isomorphism. This would identify symplectic cohomology with the Hochschild cohomology of the Fukaya category and give the latter a geometric interpretation; the source presents the assertion as unproved.