Edit: whoa, they really buried the lede: the upper bound for the knowable values may be as low as BB(1919) as of May 15!
I'm confused by the winning TM given for BB(2). It has 3 non-halt states, but N==2 should be a TM with 2, shouldn't it?
Did they merely put the illustration for BB(3) in the wrong place?
Edit: yeah, looks like they just put the illustration for BB(3) in the wrong place: https://en.wikipedia.org/wiki/Turing_machine#/media/File:Sta...