7 problems

Berstein's conjecture. The interval

Threshold conjecture. One has

Exact Hausdorff distance conjecture. The Hausdorff distance between $M$ and $L$ is precisely $\delta_0$.

Let $L$ be the classical Lagrange spectrum, let $t_1$ be the first transition point, and let $delta>0$. The first transition point is defined by … where…

Post-transition interior conjecture. For every $\epsilon>0$,

Moreira's question. For every $\delta>0$, one has

Lowest-accumulation-point conjecture. The upper BL spectrum of three-interval exchanges below $6$ is strictly included in twice the Lagrange spectrum below $3$; moreover, $6$ is th…