The Kruzkal Count is proven by the fact that eventually all numbers cross a point where some previous number has already been, which is to say they eventually s

The Kruzkal Count is proven by the fact that eventually all numbers cross a point where some previous number has already been, which is to say they eventually settle on one of a small number of concluding paths. It's not a proof for Collatz Conjecture, but I think eventually we'll find that it works out that way. Certainly in practice it does (so far). The (3x+1) is the only part that gives a smidgen of doubt, until it is eventually proven that it never takes such an extreme numerical path that it never reconverges with the CC's inevitable small number of concluding paths.