Lin's cosmetic crossing conjecture for knots

Let $K\subset S^3$ be an oriented knot and let $D\subset S^3$ be an oriented disk intersecting $K$ in two points of opposite sign. A crossing change on $K$ is the operation of performing $\pm1$-surgery on the unknot $\partial D$; it is cosmetic if the resulting oriented knot is equivalent to $K$, and nugatory if $\partial D$ bounds a disk in $S^3-K$. Cosmetic crossing conjecture. Any cosmetic crossing change is nugatory. This conjecture, attributed to X. S. Lin, is a central problem in knot theory. The paper proves it for a five-parameter infinite family of pretzel knots and discusses its status for alternating knots with eleven crossings, but it remains open in general.