Collatz Conjecture resolved : Formal Resolution by Structural Dynamics and Symbolic Folding

Introductory Note I have strong reasons to believe I have resolved the Collatz (Syracuse) conjecture. The core theorem presented here is symbolically formalized, structurally coherent, and has shown high resistance to AI-based falsification attempts. The original preprint — published on July 15, 2025 — has achieved an exceptional engagement ratio : 300 downloads for 260 views in just 10 days, indicating both academic traction and conceptual impact. This document gathers only the essential elements: – Coq & Lean codes intended for unshackled proof assistants (refer to the attached document titled Declaration) – 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