Collatz Conjecture (resolved) — Formal Resolution by Structural Dynamics and Symbolic Folding

Introductory Note I have strong reasons to believe I have resolved the Collatz conjecture. The core theorem presented here is symbolically formalized, structurally coherent, and has shown high resistance to AI-based falsification attempts. It is also compatible with formal verification in Lean. The original preprint — published on July 15, 2025 — has achieved an exceptional engagement ratio : 155 downloads for 183 views in just 9 days, indicating both academic traction and conceptual impact. This document gathers only the essential elements: – the formal theorem – the core contraction diagram (odd vortex and symbolic folding) For extended content and background, refer to : - Preprint titled “Syracuse (Collatz) Conjecture SOLVED by Hassan Takhmazov: Complete Proof” This first publication contains the complete structural proof, Lyapunov function, symbolic folding model, and IPPI structure. It includes the final theorem in both English and French, along with the earlier developmental versions. https://zenodo.org/records/15924746 - Second publication (Extended) titled “Collatz Proof by Takhmazov: Additional Content” This second release expands on the Infinity Fold metaphor, provides an annotated contraction diagram, and introduces complementary structural lemmas. https://zenodo.org/records/16241529