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Within the soft intervention setting,8 Augmented MAGs actually do not lose information with respect to the tests we consider. Your observation that the assumption is23 required in the proof of Theorem 4 is correct. Without this assumption, the proposed characterization would still24 apply under adifferent F-node construction: Instead ofanF-node foreverysymmetric difference, wewould usean25 F-node forthevariables whose mechanism differacross interventions. Therefore, faithfulness involving F-nodes does notarise inourapproach. Advantages over [9]: To the best of our knowledge, Theorem 2 in the paper is the first characterization of an32 interventional equivalence classunder causal insufficiency(presence oflatents).