On the Universality of Round Elimination Fixed Points

Recent work on distributed graph algorithms [e.g. STOC 2022, ITCS 2022, PODC 2020] has drawn attention to the following open question: are round elimination fixed points a universal technique for proving lower bounds? That is, given a locally checkable problem \(\Pi\) that requires at least \(\Omega(\log n)\) rounds in the deterministic LOCAL model, can we always find a relaxation \(\Pi'\) of \(\Pi\) that is a nontrivial fixed point for the round elimination technique [see STOC 2016, PODC 2019]? If yes, then a key part of distributed computational complexity would be also decidable.