New ask Hacker News story: I think I know why Collatz does that thing it does

I think I know why Collatz does that thing it does
2 by stuartriffle | 1 comments on Hacker News.
The normal term for this is "manic delusion of grandeur", so please help me out: 3n walks congruence classes +1 steps each one out of alignment /2 never changes that fact Accumulating co-primeness is the "memory" that stops n from repeating. This is invariant under 2^k, which allows it to make forward progress through the chaos. Exhausting congruence classes mod 3 forces n to a power of 2; game over. I asked AI to prove those things, and it did. I assume. The only question then would be if 1.5n can grow the residue vector quickly enough to outrun the exhaustive walk. I asked AI that too, and got back a one page p-word. I'm not even going to type it. I can sweet-talk AI into agreeing with damned near anything, so I'm stuck. This is the only forum I know with consistently thoughtful conversation, and I can't think my way out of this one, and I have real work to do. Is there a mathematician in the house?

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