Ribbon concordance minimality of positive knots

Prove that every positive knot in S^3 is minimal with respect to the ribbon concordance partial order; specifically, establish that if there exists a ribbon concordance from a positive knot K1 to a knot K0 (denoted K0 ≤ K1), then K0 is isotopic to K1.

Background

Ribbon concordance induces a partial order on knots in S^3 (Agol), and Gordon proved that torus knots are minimal under this order. Positive knots are those admitting a diagram with all crossings positive; torus knots are positive, suggesting a broader minimality phenomenon.

Motivated by these observations, the author and Greene formulated the conjecture that all positive knots are ribbon concordance minimal. Previous results established the conjecture for certain families (e.g., fibered positive knots and positive two-bridge knots), and this paper proves it for a large class of positive knots and provides further evidence toward full generality.