Fresse's bar-cobar equivalence conjecture for $E_n$-algebras

Let $A$ be an $4\mathcal E_n$ algebra, and let $B A$ denote its bar construction, regarded as an $4\mathcal E_{n-1}$ Hopf algebra. Let $\Omega B A$ be the cobar construction applied to $B A$, regarded as an $4\mathcal E_n$ algebra. Fresse's conjecture. The $\mathcal E_n$ algebras $\Omega B A$ and $A$ are equivalent. The conjecture is a classical theorem for $n=1$, and remains open for $n\geq 3$.