What an excellently well written paper! It does all the basics right - describes it's objective, the domain of the problem, a quick example (Rush hour) to nudge some intuition toward the reader, before going on to prove undecidability. It even tackles the decidability of another "should-obviously-work" (Bounded braid) idea that the author had (turns out to be decidable).

Also, I wonder if most programmers have unknowingly built a ton of Braid intuition because of the way the time reversal tree matches the way we model the undo tree in $EDITOR.