Qazaqzeh–Chbili–Lowrance conjecture on adequacy and Turaev genus

Let $L$ be a non-split link. Write $c(L)$ for its crossing number, $g_T(L)$ for its Turaev genus, and $v_L(t)$ for its Jones polynomial. Qazaqzeh–Chbili–Lowrance conjecture. The link $L$ is adequate if and only if

$$\operatorname{span}(v_L(t))=c(L)-g_T(L).$$

The conjecture characterizes adequate links through the span of the Jones polynomial, crossing number, and Turaev genus. This paper verifies it for a family of Turaev genus $2$ links, while the general statement remains open.