An approach to the Syracuse conjecture v. 2

I propose a new approach to the Syracuse conjecture by introducing a tree structure T which integrates all the natural integers. This construc- tion makes it possible to show that any number necessarily follows a path leading to 1 and can be an interesting way of validating the conjecture. In addition, to reinforce the main argument of the paper, namely that the T-Tree can be used to prove Syracuse’s conjecture, I will introduce a first appendix that will provide a concrete visualisation of the distribution of Buds in the Tree. It will show how the mathematical rules defined in the previous sections translate into an organised structure that includes all odd integers. I will introduce the concept of Arborescent Number in Appendix 2 then, in Appendix 3, I will provide a python code that NEW : Finally, in Appendix 4, I will try to prove by recurrence that every positive odd number is a bud of T