The directional weak-mixing conjecture for translation surfaces

Let $X$ be a translation surface, and suppose that $X$ does not factor over the circle ${\mathbb T}={\mathbb R}/{\mathbb Z}$; in particular, suppose that $X$ is not a torus cover. For a direction on $X$, consider the associated translation flow. A property is directionally typical if it holds for almost every direction.

Directional weak-mixing conjecture. For every translation surface that does not factor over the circle, the directionally typical translation flow is weakly mixing.

Weak mixing is known for Masur–Veech typical translation flows and in several higher-rank and rank-one settings, but the presence of exceptional surfaces makes the general characterization difficult. The conjecture remains open.