5 problems

Extension conjecture. An $X$-valued holomorphic function $f$ on $U$ admits a continuous extension to $\widehat U$ if and only if $f(V)\Subset X$ for every subset…

Brahmagupta-move staircase conjecture. The functions $c_{\beta_i}$ have infinite staircases.

Inner-corner obstruction conjecture. At these intersections,

Staircase correspondence conjecture. For every $\beta\geq\sqrt{3}$, the function $c_\beta$ has an infinite staircase if and only if the function $c_{H_b}$ has an infinite staircase…

Let $n\geq 2$ and $k\geq 0$. For each $i\geq 0$, let $A_{i,n}^{(k)}$ and $\hat{A}_{i,n}^{(k)}$ be the associated classes, and let $C_{L_{n,k}}(\alpha)$, $L_{n,k}$, $c_{i,n,k}$,…