Goncharov's isomorphism conjecture for the dihedral and motivic Lie coalgebras

Let $\nu_{\bullet,\bullet}^{\cal M}(\mu_N):{\cal D}_{\bullet,\bullet}(\mu_N)\longrightarrow {\cal C}_{\bullet,\bullet}^{\cal M}(\mu_N)$ be the canonical surjective homomorphism of bigraded Lie coalgebras from the dihedral Lie coalgebra to the motivic Lie coalgebra. Here $N$ is a positive integer, and $w$ and $m$ denote the weight and depth, respectively.

Goncharov's isomorphism conjecture. The map $\nu_{\bullet,\bullet}^{\cal M}(\mu_N)$ is an isomorphism for either $N=1$, or $N=p$ is a prime and $w=m$.

The assertion predicts that the dihedral relations give all relations in the indicated motivic settings. The supplied text does not state whether this conjecture has been resolved.