Winding number m and -m patterns acting on concordance

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We prove that for any winding number m>0 pattern P and winding number -m pattern Q, there exist knots K such that the minimal genus of a cobordism between P(K) and Q(K) is arbitrarily large. This answers a question posed by Cochran-Harvey [CH17] and generalizes a result of Kim-Livingston [KL05].