Goncharov's regulator image conjecture

Let $X$ be a variety over $\mathbb{Q}$, and suppose the regulator map is

$$H^i\Gamma(X;n)\longrightarrow H^i_{\mathcal{D}}(X\otimes_{\mathbb{Q}}\mathbb{R}/\mathbb{R};\mathbb{R}(n)).$$

Here $H^i_{\mathcal{D}}$ denotes Deligne cohomology, and the map is the regulator map constructed from the polylogarithmic complex.

Goncharov's regulator image conjecture. The image of this regulator map in Deligne cohomology coincides with the image of Beilinson's regulator map.

The claim predicts that the explicitly constructed polylogarithmic regulator has exactly the same image as Beilinson's regulator. The source gives no evidence of a general resolution status.