I've been looking at that particular rabbit hole since a professor of mine mentioned it in 2003 or something. Once or twice a year, I'll read about some theorem or something and think it can be applied to Collatz somehow and dive back in.

I've actually proved it several times...except for the insignificant detail that I glossed over that didn't seem important but tanks the proof.

Someday I'll have to publish my "book of lemmas that don't prove the collatz conjecture."