[sligocki]

I'm the author. That's a great summary of the background, thanks! As you say, this post is extremely in the weeds analyzing a single Turing Machine's behavior. I wrote this post mainly aimed at people in the bbchallenge.org project or who have spent time analyzing Skelet's machines previously.

In addition to proving this one machine by hand (which may be necessary to completely prove the BB(5) value), this post also introduces a new type of proof that a TM does not halt (specifically the "Reset Invariant"). There's potential that this technique could be automated to prove a whole group of TMs non-halting (which is the main way that we have made progress on proving Busy Beaver values in the past).