Goncharov's universality conjecture for motivic iterated integrals

Let $F$ be a number field. For elements $a_0,\ldots,a_{n+1}\in F$, let

$$\mathbb{I}^{\mathcal{H}}(a_0;a_1,\ldots,a_n;a_{n+1})\in\mathcal{H}_n(F)$$

be the motivic iterated integral associated with the corresponding motivic fundamental groupoid, and let $\mathcal{H}(F)$ be the motivic Hopf algebra. Goncharov's universality conjecture. The motivic iterated integrals $\mathbb{I}^{\mathcal{H}}(a_0;a_1,\ldots,a_n;a_{n+1})$, for all choices of $a_i\in F$, span $\mathcal{H}(F)$. If true, motivic fundamental groups would generate the category of mixed Tate motives as a tannakian category; the source does not specify a resolution.