Uniqueness conjecture for positive knots in smooth concordance classes

A smooth concordance class is an equivalence class of knots under smooth concordance. A knot is minimal with respect to ribbon concordance if no distinct knot lies below it in the ribbon-concordance order. Uniqueness conjecture for positive knots. Every smooth concordance class contains at most one positive knot. Stoimenow previously conjectured that each concordance class contains finitely many positive knots, and that weaker statement was proved by Baader, Dehornoy, and Liechti. The stronger uniqueness statement remains open and is related to Gordon's questions about minimal representatives.