Alternating-knot unknotting-crossing conjecture

Let $K\subset S^3$ be an alternating knot, and let an alternating diagram be a diagram in which over- and under-crossings alternate along each component. An unknotting crossing is a crossing whose change produces the unknot. Alternating-knot unknotting-crossing conjecture. If $u(K)=1$, then every alternating diagram of $K$ contains an unknotting crossing. For alternating knots, minimal diagrams are alternating and are related by flypes and nugatory crossing moves, which preserve this property. The paper proves this assertion for alternating 3-braid knots; in the stated generality here it is presented as a conjectural derivative of Kohn's conjecture.