Overview of the Collatz arguments

There’s no recursion, it can’t runaway to infinity, and it can’t lazily meander around some value for infinity either. Since there’s also no repetition in the odd outputs (or there would be recursion) the Collatz algorithm will sequence through every odd possibility for a given bounded set of odds. Since the Collatz algorithm can’t also run to infinity, then it will run through a given sequence of all odd possibilities. The completion of which can only be halted by a power of 2. This can lead to a lower odd value that runs through another sequence of bounded odds, or a number whose factors are only powers of 2.
And that’s the truth of the Collatz Conjecture if not a formal proof, yet..