The free-loop-space Hochschild cohomology Gerstenhaber algebra isomorphism conjecture

Let $M$ be a compact oriented $d$-dimensional smooth manifold, let $LM=map(S^1,M)$ be its free loop space, and let $S^*(M)$ denote the differential graded algebra of singular cochains on $M$. Write $H_{*+d}(LM)$ for shifted free loop homology and $HH^*(S^*(M);S^*(M))$ for Hochschild cohomology. Gerstenhaber algebra isomorphism conjecture. If $M$ is simply connected, then there is an isomorphism of Gerstenhaber algebras

$$H_{*+d}(LM)\cong HH^*(S^*(M);S^*(M)).$$

This conjecture proposes the algebraic realization of the Chas–Sullivan Gerstenhaber structure on free loop homology through Hochschild cohomology. The source attributes it to Chas and Sullivan or Cohen and Jones, and does not state whether it has been resolved.