Goncharov’s universality conjecture for motivic iterated integrals

Show that, for a number field F, the motivic iterated integrals I^H(a_0; a_1, …, a_n; a_{n+1}) attached to all choices of points a_i ∈ F on P^1_F span the motivic Hopf algebra H(F); equivalently, establish that motivic fundamental groupoids O(π_1^mot(P^1_F \ {a_i}, a_0, a_{n+1})) generate MT(F) as a tannakian category.

Background

Iterated integrals on punctured projective lines give rise to motivic fundamental groupoids whose periods include classical and multiple polylogarithms. Their motivic versions define elements of the Hopf algebra H(F).

The conjecture posits that these motivic iterated integrals suffice to generate the entire Hopf algebra, providing a universal construction of mixed Tate periods over F and, tannakianly, generating MT(F).