Ribbon knots and iterated cables of fibered knots

We define a knot to be γ ₀ γ 0 - sharp if its Seifert genus is detected by the concordance invariant γ ₀ γ 0 , which arises from the immersed curve formalism in bordered Heegaard Floer homology. We show that a connected sum of γ ₀ γ 0 -sharp fibered knots is ribbon exactly when it is of the form K # -K K # - K . Consequently, either iterated cables of tight fibered knots are linearly independent in the smooth concordance group, or the slice–ribbon conjecture fails.