An approach to the Syracuse conjecture

I propose an approach to the Syracuse conjecture by introducing a tree structure T which integrates all the natural integers. This construction 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 generates the Arborecent Number and the Generation of a given Bud. Warning: This text does not claim to be a rigorous scientific contribution. It is important to note that I do not cite any mathematical article recognised by the community and I cannot claim to be a mathematician myself. My aim here is to share my personal vision of the Syracuse problem. I am not at all sure of the originality or relevance of this approach. By publishing my article, I simply hope to elicit reactions from real mathematicians if my approach proves to be even remotely interesting or innovative; that would already be an unexpected joy for me! I’m well aware that, once again, nothing here has been rigorously demonstrated!