A possible solution for Collatz conjecture

I found a possible solution to sloved collatz conjecture.

1. In the definition f of Collatz conjecture is not the target problem we need to slove.
I introduce a function F to make it recursive.

 

2. In the general binary number convertion of nature number, we can transform any number to this form:

3. and I convert to binary version

4.and check complex version of function

my idea is simple:

if two kind of function: Collatz map and "shortcut" relation Collatz map are same

it's must const[F(z)=c]

It's means this problem may reduce to two version of Collatz map is same, they will be proof.

And the definition of problem is not Collatz map's f, but (differencial version) difference equation version.