Deligne–Ihara structural conjectures for Galois image Lie algebras

Let $l$ be a prime, let $\mathfrak g^l_\bullet$ be the graded Lie algebra over $\mathbb Q_l$ associated with the Galois image acting on the pro-$l$ fundamental group of $\mathbb P^1_{\overline{\mathbb Q}}-\{0,1,\infty\}$, and let $\mathfrak D_\bullet$ be the stable derivation algebra over $\mathbb Q$. There is an embedding

$$\varPsi_l:\mathfrak g^l_\bullet\hookrightarrow\mathfrak D_\bullet\otimes_{\mathbb Q}\mathbb Q_l.$$

Deligne–Ihara conjectures. The embedding $\varPsi_l$ is an isomorphism for every prime $l$; the Lie algebras $\mathfrak g^l_\bullet$ and $\mathfrak D_\bullet$ are free; and their generators may be chosen with one element in every odd degree $m=3,5,7,\ldots$. These conjectures describe the expected common free graded Lie-algebra structure underlying the $l$-adic Galois images and the stable derivation algebra. The source attributes them to Ihara and Deligne and treats them as open.