An interesting thing about this is that they figured out a high-level description of what this Busy Beaver program is doing - it's computing a Collatz-like sequence until it terminates.
I'm not sure if that is described in this paper, but I learned about it in this Scott Aaronson talk,
https://www.youtube.com/watch?v=VplMHWSZf5c
e.g see the slide at 31:40.
Collatz-like except on one critical aspect: it is known to terminate!
Interesting, it seems like a possible contender for BB6 (“Antihydra”) also does something Collatz-like. Is Collatz just a good blueprint for constructing long, complex, finite sequences?
I find it very interesting as well. One would think that there might be many problems with similar properties, but people have already discovered the one that surfaces in Turing machines as well. Does this suggest that there are not that many problems with this type of property? Or does it suggest that we stumbled upon the simplest case.