Goncharov's freeness conjecture for the motivic Galois Lie algebra

Let $\ell$ be a prime, let ${\mathbb Q}(\mu_{\ell^\infty})$ be the cyclotomic extension of ${\mathbb Q}$, and consider the action of its Galois group on the ${\ell}$-adic unipotent completion of the fundamental group of ${{\mathbb P}^1-\{0,1,\infty\}}$ based at $\overrightarrow{01}$. Let $\mathfrak g$ be the Lie algebra of the Zariski closure of this Galois image in the automorphism group.

Goncharov's conjecture. The Lie algebra $\mathfrak g$ is a prounipotent Lie algebra freely generated by elements $z_3,z_5,z_7,\dots$, where $z_m$ has weight $-2m$.

The conjecture is a freeness strengthening of Deligne's generation conjecture. The supplied status evidence says that the generation part is proved in Hain--Matsumoto, but does not state that the freeness assertion is proved; accordingly, the full conjecture is recorded as open.