[LegionMammal978]

Hmm, around n = 2 or k = 2, there are only 2 added transitions for a machine to do "the next big thing" googologically, so that doesn't leave much slack for many different machines at the same level. But maybe that could happen closer to the n = k line, where each increment adds many new transitions. Or to the contrary, maybe each increment just does several "next big things".

[cwillu]

Or the next big things were implementable at n-3, but finally pay off at n+1?