Goncharov's kernel conjecture for polylogarithmic groups

Let $F$ be a field, let $B_n(F)$ be Goncharov's polylogarithmic group, and let

$$\delta_n:B_n(F)\to B_{n-1}(F)\otimes F^\times_\mathbb Q$$

be the associated map. Write $K^{(n)}_{2n-1}(F)_\mathbb Q$ for the $n$-th graded quotient of the $\gamma$-filtration on $K_{2n-1}(F)_\mathbb Q$. Goncharov's conjecture. There is an isomorphism

$$\operatorname{ker}(\delta_n)\simeq K^{(n)}_{2n-1}(F)_\mathbb Q.$$

This conjecture relates the kernel of the polylogarithmic co-Lie differential to the appropriate graded piece of algebraic $K$-theory; its status is not determined in the supplied text.