For non-experts it would have helped if you had explained the problem. For those who don't know, the problem is stated as:

Take any positive integer x

If it is even halve it

If it is odd, replace it by 3x+1

Repeat

The conjecture is that you will always end up with the repeated sequence 4, 2, 1, ...

However, the author has not solved it, he has merely written some intellectual sounding waffle that doesn't really mean anything.