Goncharov's algebraic structure conjecture for multiple zeta values

Let ${\cal Z}$ be the commutative algebra over $\mathbb Q$ spanned by multiple zeta values, and let ${\cal Z}_k$ denote its weight-$k$ subspace. Let ${\cal F}(3,5,...)_{\bullet}$ be the free graded Lie algebra generated by elements $e_{-(2n+1)}$ of degree $-(2n+1)$ for $n\geq 1$, and let $U{\cal F}(3,5,...)_{\bullet}^{\vee}$ be the graded dual of its universal enveloping algebra, with $\pi^2$ assigned degree $2$. Goncharov's conjecture. The weight provides a grading on ${\cal Z}$, and there is an isomorphism of graded algebras over $\mathbb Q$:

$${\cal Z}_{\bullet}\cong \mathbb Q[\pi^2]\otimes_{\mathbb Q}U{\cal F}(3,5,...)_{\bullet}^{\vee}.$$

This conjecturally gives the complete algebraic structure and all algebraic relations among multiple zeta values.