3 problems

Slope-signature deviation conjecture. There are constants $b$ and $c$ such that, for any hyperbolic knot $K$ in $S^3$,

Asymptotic sign conjecture. If $K$ is a hyperbolic knot in $S^3$ with $|\widehat{\sigma}(K)|>1$, then $\sigma(K)$ and $\operatorname{Re}(\mu(K))$ have the same sign asymptotically…

Let $L$ be a non-split link of Turaev genus one. Write $Kh^{i,j}(L)$ for its Khovanov homology, let $j_{\min}(L)$ and $j_{\max}(L)$ denote the minimum and maximum quantum gradings…