The k-formality conjecture for hyperpolygonal arrangements

For $n\in{\mathbb N}$, let ${\mathscr H}_n$ denote the hyperpolygonal arrangement. An arrangement is $k$-formal when it has the stronger formality property indexed by $k$, with $1\leq k\leq\operatorname{rk}({\mathscr H}_n)$. The k-formality conjecture. For any $n\in{\mathbb N}$, the arrangement ${\mathscr H}_n$ is $k$-formal for any $k$. This is motivated by computational evidence for further non-free hyperpolygonal arrangements and by the fact that free arrangements are $k$-formal for all $k$.