Open dense full-measure conjecture for finite-type double rotations

Let $\mathcal{V}$ be the parameter space of pairs ${v_0,v_1}$, with a fixed partition, for which the double-rotation map $f_{v_0,v_1}$ on a two-dimensional torus is of finite type. Open dense full-measure conjecture. $\mathcal{V}$ is an open, dense, and full-measure subset of the set of all parameters. This is a stronger formal formulation of the paper’s simulation-based expectation that double rotations are finite type for almost every parameter; the source provides no proof.