Champanerkar–Kofman–Purcell volume–determinant conjecture for alternating knots

Let $K$ be a hyperbolic alternating knot. Here, $\operatorname{vol}(K)$ denotes the hyperbolic volume of the complement $S^3\backslash K$, and $\det(K)$ denotes the determinant of $K$. Champanerkar–Kofman–Purcell conjecture.

$$\operatorname{vol}(K) < 2\pi \log \det(K).$$

The conjecture proposes a relationship between the hyperbolic geometry and combinatorial topology of alternating knots. The source states that it is proved for 2-bridge links, alternating 3-braids, and several other infinite families, while the general case remains open.