OT: status of my Collatz solution

[Rudy Toody]

I have started my paper and I am nailing down all the definitions as I go along.

My breakthrough was a few days ago with this function.

 

[biodoc]

Good luck RT! :thumbsup:

 

[Ken g6]

Doesn't look like it would apply to the Collatz DC project, but looks like a good step toward proving the overall conjecture. 🙂 I think the only thing left would be proving there's no infinitely increasing sequence.

 

[Rudy Toody]

Doesn't look like it would apply to the Collatz DC project, but looks like a good step toward proving the overall conjecture. 🙂 I think the only thing left would be proving there's no infinitely increasing sequence.

We are pinning down local non-looping and local non-runaway. The local non-looping means that a descender that terminates a finite ascending sequence does not loop-back to any of those ascenders. The local non-runaway is shown by the finite ascending sequences.

Yet to be addressed is the chaining of these finite sequence: do they loop or runaway?

The rigidity of the method we are using to show this might also take care of chaining. It is a pretty deep concept, so it will take some time to get it right.

If the rigidity technique is successful, it will have some bearing on types of P vs NP problems.