Zagier's conjecture on motivic Ext groups and single-valued unipotent polylogarithms

Let $K$ be the field appearing in the motivic category, and for each integer $n\geq 2$ write

$$E_n:=\operatorname{Ext}^1_K(\mathbb{Q}(0),\mathbb{Q}(n)).$$

For $t\in K$, let $\operatorname{Li}_n^{U,sv}(t)$ denote the single-valued unipotent $n$-logarithm. Zagier's conjecture. For every $n\geq 2$, the group $E_n$ is spanned by the elements $\operatorname{Li}_n^{U,sv}(t)$ with $t\in K$.

The conjecture is known for $n=2$ and $n=3$, and for cyclotomic fields $K$. Outside the cyclotomic case, the source notes that explicit conjectural constructions of elements of $E_n$ are largely unavailable, so the general statement remains open.