The alternating-diagram maximal volume conjecture

Let $K$ be an alternating hyperbolic knot, and let $K'$ be obtained from $K$ by changing crossings in a diagram. The alternating-diagram maximal volume conjecture. (a) If any crossing of $K$ is changed, then

$${\rm vol}(K')<{\rm vol}(K).$$

(b) The same inequality holds when any proper subset of crossings of $K$ is changed. The conjecture concerns whether alternating diagrams maximize hyperbolic volume among diagrams with a given projection. Part (a) has been verified for all alternating knots up to 18 crossings, while part (b) remains open; under twisting on two strands, the volume difference can nevertheless be arbitrarily small and positive.