4 problems

Higher special-point obstruction conjecture. For $i>1$, $c_{H_b}$ has no descending staircase. Furthermore, there exists $\varepsilon>0$ such that, for

Continued-fraction length conjecture. (i) The continued-fraction expansion of the center $p/q$ of ${\bf E}_{\delta}$ has $CF$-length…

Obstruction conjecture for special rational staircases. For all such special $b$, the capacity function should be given by this obstruction at points just above the corresponding s…

Special-rational-point conjecture. No special rational point has a staircase. This question is related to whether $b=1/3$ has a descending staircase.