Surjectivity of linear higher Chow cycles for number fields

For a number field $k$, let $\mathrm{CH}^n(k,2n-1)_{\mathbb{Q}}$ be the simplicial higher Chow group and let $\mathrm{LCH}^n(k,2n-1)_{\mathbb{Q}}$ be the image of the canonical homomorphism

$$\psi_n:H_{2n-1}(\mathrm{GL}_n(k),\mathbb{Q})\longrightarrow \mathrm{CH}^n(k,2n-1)_{\mathbb{Q}}.$$

The linear higher Chow cycles are expected to surject rationally onto the simplicial higher Chow groups. Surjectivity conjecture. The homomorphism $\psi_n$ is surjective for every $n\geq 1$.

This conjecture asks whether the cycles arising from linear configurations account for all rational higher Chow classes of a point over a number field. It is presented as the simplest test of the proposed relationship between linear higher Chow groups, the Beilinson regulator, and Borel classes; no resolution is given in the source.