Białynicki-Birula linearization conjecture for free associative algebras

Let $F_n=\mathbb{K}\langle x_1,\ldots,x_n\rangle$ be the free associative algebra, and let $\mathbb{T}_{n-1}$ be the $(n-1)$-dimensional algebraic torus. Free-associative torus-action linearization conjecture. Every effective action of $\mathbb{T}_{n-1}$ on $F_n$ is linearizable. This is proposed as the free associative analogue of the second Białynicki-Birula theorem; no resolution is given in the supplied text.