Torisu's unknotting-number-one conjecture for three-branched Montesinos knots

Let $K$ be a Montesinos knot with three branches. Here $M(0; (p,r),(q,s),(2mn\pm 1, 2n^2))$ denotes the Montesinos knot with the displayed parameters. Torisu's conjecture. The knot $K$ has unknotting number one if and only if

$$K=\mathcal{M}(0; (p,r),(q,s),(2mn\pm 1, 2n^2)),$$

where $p,q,r,s,m$ and $n$ are non-zero integers, $m$ and $n$ are coprime, and $ps+rq=1$. This gives a conjectural classification of the three-branched Montesinos knots with unknotting number one; Montesinos knots with four or more branches are known not to have unknotting number one, while the three-branch case remains the subject of this conjectural list.