Patterns of resemblance and Bachmann-Howard fixed points

Timothy Carlson’s patterns of resemblance employ the notion of Σ₁-elementarity to describe large computable ordinals. It has been conjectured that a relativization of these patterns to dilators leads to an equivalence with π¹₁ -comprehension (Question 27 of A. Montalbán's "Open questions in reversemathematics",Bull.Symb. Log. 17(3)2011, 431-454). In the present paper we prove this conjecture. The crucial direction of the equivalence (towards π¹₁-comprehension) is reduced to a previous result of the author, which is concerned with relativizations of the Bachmann-Howard ordinal.