A distinct proof and extension of the Collatz conjecture

A proof by contradiction of the Collatz conjecture is presented based on the constructive-topological approach using the geometric mean properties of the network structures generated by the 3n+1 algorithm. The key contradiction was revealed by the method of “constructive induction” and is related to restrictions on the divisibility of the rootless subnet. The logic of the proof is transferable to other cases, which made it possible to formulate and detail the extension of the Collatz conjecture to the entire class of similar algorithms. Contents 1. Introduction 2. Geometric mean properties 3. Proof technique 4. Logic of the proof 5. Extension of the Collatz conjecture 6. Conclusion