The Deligne–Ihara conjecture for the thrice-punctured projective line

Let $T=\mathbb{P}^{1}_{\mathbb{Q}}-\{0,1,\infty\}$, and let $\mathfrak{t}=\bigoplus_{m>0}\mathfrak{t}_m$ be the graded Lie algebra over $\mathbb{Z}_p$ associated with the lower central filtration on the pro-$p$ fundamental group of $T$. The Deligne–Ihara conjecture. The graded Lie algebra $\mathfrak{t} \otimes \mathbb{Q}_{p}$ is freely generated by one element in each odd degree $>1$. This conjecture is presented as a standard formulation in the case of the thrice-punctured projective line; the supplied text gives no resolution status.