Collatz Proof by Takhmazov : additional content

Hi, I have no formal training in mathematics or science. I work with mathematical intuition, structural logic, and a symbolic reading of number behavior. It was not technical reasoning that guided me, but a deep conviction: Infinity can be folded in half, like a sheet of paper. That insight opened a new path to a complete, rigorous, and fully formalizable demonstration. It began with drawings. I traced arrows, motifs, and symbolic blocks. And I noticed a recurring, inescapable structure: the odd vortex. Then came the physical intuition: If I can fold any number back toward the center — like folding a sheet of paper — then infinity becomes accessible. This gave birth to the Infinity Fold Experiment, a physical metaphor turned symbolic tool. Each number folds, folds again, and eventually loses its capacity to unfold: it is absorbed. But through this process, I perceived a fractal symmetry: As if, by folding a distant IPPI motif toward the boundary, I was activating a structural field — a vortex capable of devouring an odd number, then infinitely recycling it by reinjecting it into the loop 4 2 1 4, which becomes the canonical square of the system. This vortex acts as a dynamic matrix: it structures, absorbs, simplifies. This republication contains : Infinity Fold Experiment (annotated version + contraction diagram) Main theorem proving the Collatz conjecture (structural proof using block dynamics and Lyapunov function) Complementary lemmas based on structural intuition and the vortex For intermediate stages and the first appearance of the theorem: 🔗 https://zenodo.org/records/15924746 takhmazovsyracuseatyahoodotcom EDIT: Attempts at copying are starting to appear (that’s a good sign — it means I’ve succeeded!) : /web/20250730111448/https://www.youtube.com/watch? app=desktop&v=8T5U09mMcYc https://web.archive.org/web/20250730115737/https://www.researchgate.net/publication/393515166_A_Mirror-Modular_Spine_Solves_the_3x_1_Collatz%27s_Puzzle?channel=doi&linkId=686e230439c35835120819a6&showFulltext=true For more information, refer to the attached document titled "Rapport de défense".