The Conway–Kinoshita–Terasaka chord-diagram inequivalence conjecture

Let $C$ and $KT$ be the chord diagrams arising from the planar projections of the Conway and Kinoshita–Terasaka knots, respectively. These are degree-11 chord diagrams with the same intersection graph.

Conway–Kinoshita–Terasaka conjecture. The chord diagrams $C$ and $KT$ are not equivalent.

The proposed pair would provide an explicit counterexample to the intersection graph conjecture at degree $11$. The source reports that the general conjecture fails at degree $11$, although at the point of this statement no explicit inequivalent pair had been exhibited; the supplied status evidence confirms that this conjecture is disproved.