Free associative Białynicki-Birula linearization conjecture

Let $F_n=\mathbb{K}\langle x_1,\ldots,x_n\rangle$ be the free associative algebra, and let $\mathbb{T}_{n-1}$ act effectively on $F_n$. Free associative Białynicki-Birula conjecture. Every effective action of $\mathbb{T}_{n-1}$ on $F_n$ is linearizable. The paper calls this the free associative analogue of the second Białynicki-Birula theorem; it is posed as an outstanding problem and no resolution is given.