The genus bound for the theta knot invariant

Let $K$ be a knot and let $g(K)$ denote its genus. The Laurent polynomial $\theta(K)$ has degree in $T_1$ satisfying

$$\deg_{T_1}\theta(K)\leq 2g(K).$$

Genus bound conjecture. For every knot $K$, the displayed inequality holds. The conjecture has been verified for all knots with up to 13 crossings, but remains unproved in general; it can give a stronger genus bound than the Alexander polynomial.