The Andreadakis conjecture for automorphism groups of free groups

Let $F_n$ be the free group of rank $n$, let $\mathrm{IA}_n=\mathcal{A}_n'(1)$ be the group of automorphisms of $F_n$ acting trivially on its abelianization, and let

$$\mathcal{A}_n'(1)\supset\mathcal{A}_n'(2)\supset\cdots$$

be the lower central series of $\mathrm{IA}_n$. Let $\mathcal{A}_n(1)\supset\mathcal{A}_n(2)\supset\cdots$ be the Andreadakis–Johnson filtration of $\mathrm{IA}_n$; since this is a central filtration, $\mathcal{A}_n'(k)\subset\mathcal{A}_n(k)$ for every $k\geq 1$. The Andreadakis conjecture. For any $n\geq 3$ and $k\geq 1$,

$$\mathcal{A}_n'(k)=\mathcal{A}_n(k).$$

The conjecture asks whether the lower central series and the Andreadakis–Johnson filtration of $\mathrm{IA}_n$ coincide in every degree for free groups of rank at least three. The supplied source does not state a resolution, so the status is left open.