The Gerstenhaber algebra conjecture for singular cochains and free loop homology

Let $M$ be simply connected and let ${\Bbbk}$ be a field. Let $LM=map(S^1,M)$ be the free loop space, let $d$ be the dimension parameter of $M$, and let $S^*(M)$ denote the algebra of singular cochains on $M$. The Gerstenhaber algebra conjecture. There is an isomorphism of Gerstenhaber algebras

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

This is the cochain-side counterpart to the proposed identification using singular chains on a topological group. The supplied text does not state whether this conjecture has been resolved.