Upon re-reading the paper, I also noticed that it says "In the beginning of the Propose step the [deterministically chosen] designated proposer for that round broadcasts a proposal to its peers via gossip" but it's not obvious to me what happens if that proposer fails to participate. Is the algorithm allowed to skip to the next round? If so, is there some guarantee that the gaps can't later be filled in, and the history retroactively modified? (The DLS algorithm solves this problem by requiring all nodes to propose a value.)