Breadth–determinant conjecture for quasi-alternating links

Let $L$ be an oriented link. The breadth of its Jones polynomial $V_L(t)$, denoted by $\operatorname{breadth} V_L(t)$, is the difference between the highest and lowest degrees of $t$ appearing in $V_L(t)$.

Breadth–determinant conjecture. If $L$ is a quasi-alternating link, then

$$\operatorname{breadth} V_L(t) \leq \det(L).$$

This conjecture is weaker than the crossing-number inequality $c(L)\leq \det(L)$ because the breadth of the Jones polynomial is always at most the crossing number. It is known for all checked quasi-alternating links satisfying that crossing-number inequality, and is proved in the source for quasi-alternating closed $3$-braids; its general status remains open.