The pure twin group right-angled Artin group conjecture

Let $T_n$ be the twin group, and let $PT_n$ be its pure subgroup, defined as the kernel of the natural surjection $T_n\to S_n$ given by $s_i\mapsto\tau_i$. A right-angled Artin group is a group admitting a presentation whose defining relations are commutators between selected pairs of generators.

Pure twin group conjecture. $PT_n$ is a right-angled Artin group for each $n\geq 3$.

The claim is known for $n=3,4,5$, while $PT_6$ is also known to be a right-angled Artin group through its description as a free product of $F_{71}$ and 20 copies of $\mathbb{Z}\oplus\mathbb{Z}$. The status for $n\geq 7$ remains open.