4 problems

For a knot $K$, let $P_+$ and $P_-$ denote the $(2,1)$- and $(2,-1)$-cable patterns, respectively, and let $P$ be any pattern. Let $s_p$ denote the Rasmussen invariant over a field…

Consecutive-torus-knot conjecture. For every integer $n\geq 2$, if

Lewark–Zibrowius conjecture. For every prime $p$ and every prime $q\ne p$,

Whitehead-double torus-knot conjecture. If $n$ is a positive integer and $K$ is the mirror of