u/Significant-Farm-884

I would like to share the first chapter of an angoing work proposes a structural study of the Collatz conjecture, reformulated under an axiomatic framework, I call (PCA, PCA1= 3n+1 for n odd.

PCA2 = n/2 for n even).The preprint IS deposited on Zenodo ( DOI: https ://doi.org/10.5281/zenodo.21927860).

This chapter does not claim a full proof of the conjecture_it establishes the structural mechanism and provides convergence to 1 for two specific geometric familis of integers.

The question of whether every natural number converges toward these familis IS left open for chapter 2.

I welcome rigorous critical Feedback in particular on the sections below

Preprint on the Collatz conjecture,structura/axiomatique approach (PCA).

DOI:

https://doi.org/10.5281/zenodo.21864709

Feedback welcome;especially on non-circularity of thé reasoning,