Goncharov's trilogarithm isomorphism conjecture

Let $F$ be an infinite field. Let $B_3(F)$ be Goncharov's Bloch group defined using the stated relations, and let $\mathcal{L}^{\mathrm{f}}_3(F)$ be the weight-three component of the formal Lie coalgebra. Goncharov's trilogarithm conjecture. The map

$$L_3\colon B_3(F)_{\mathbb{Q}}\longrightarrow\mathcal{L}^{\mathrm{f}}_3(F)$$

sending $[a]$ to $\operatorname{Li}^{\mathcal{L}}_3(a)$ is an isomorphism. The analogous weight-two map was proved immediately beforehand; the source gives no resolution evidence for the weight-three assertion.