Goncharov's motivic polylogarithmic complex conjecture

Let $\mathbb K$ be a field of characteristic zero. Motivic cohomology of the point is denoted by $H^{i,m}(\operatorname{Spec}\mathbb K,\mathbb Q)$, and $\Gamma(\mathbb K,m)$ is Goncharov's polylogarithmic complex

$$\Gamma(\mathbb K,m)\colon \mathcal B_m(\mathbb K)\xrightarrow{\delta_m} \mathcal B_{m-1}(\mathbb K)\otimes \mathbb K^\times\xrightarrow{\delta_m}\dots\xrightarrow{\delta_m}\mathcal B_2(\mathbb K)\otimes \Lambda^{m-2}\mathbb K^\times\xrightarrow{\delta_m}\Lambda^m \mathbb K^\times.$$

Goncharov's conjecture. For any field $\mathbb K$ there is a functorial isomorphism

$$H^{i,m}(\operatorname{Spec}\mathbb K,\mathbb Q)\cong H^i(\Gamma(\mathbb K,m)).$$

This conjecture proposes that the polylogarithmic complex computes the motivic cohomology of a field. The paper proves a rational comparison in degree $m-1$ and weight $m$, but the statement in all degrees remains open.