Mixing conjecture for Bratteli-diagram staircase suspensions

Let $(\mathcal{B},w^\pm, \leq_{r,s})$ be a Bratteli diagram whose positive part encodes a mixing staircase transformation, and whose negative part is given by the constant $2\times 2$ identity matrix. Let

$$\mathcal{V}_0=\{v_1,v_2\},$$

and suppose that $w^-(v_1)=p$ and $w^-(v_2)=q$ with $p/q$ irrational.

Mixing conjecture. The vertical flow on $S(\mathcal{B},w^\pm, \leq_{r,s})$ is mixing.

This claim proposes a concrete mechanism for producing mixing vertical flows on flat surfaces from mixing staircase transformations. The supplied text gives the construction and hypotheses but no evidence resolving the claim, so its status remains open.