COLLATZ-HASSE-SYRACUSE-ULAM-KAKUTANI SEQUENCE: CONVERGENCE TO THE TRIVIAL CYCLE PROVED

Abstract

This research report presents the Collatz-Hasse-Syracuse-Ulam-Kakutani (CHSUK) Theorem, which asserts the convergence of the Collatz Sequence to the trivial cycle, thus proving the Collatz Conjecture, which has been a long-standing unsolved problem.  The proof is based on the bijective isomorphism established between the set of positive integers and a carefully designed system with a hierarchy (arborescence) of binary-exponential-ladders defined on the set of positive odd numbers.  The reasoning includes a reductio-ad-absurdum argument to demonstrate domain exhaustion, logically excluding the existence of extraneous objects, such as rogue loops or infinite threads, from the conjecture’s domain.