Collatz conjecture becomes theorem

TL;DR

This paper claims to prove the Collatz conjecture by establishing an algorithmic formula for its halting property, suggesting it is a theorem within the algorithmic theory of natural numbers.

Contribution

It introduces a proof of the Collatz conjecture using an algorithmic formula, claiming to resolve a long-standing open problem.

Findings

Proves the Collatz conjecture as a theorem

Establishes an algorithmic formula for the halting property

Shows the conjecture cannot be proved in elementary number theory

Abstract

The Collatz hypothesis is a theorem of the algorithmic theory of natural numbers. We prove the (algorithmic) formula that expresses the halting property of Collatz algorithm. The observation that Collatz's theorem cannot be proved in any elementary number theory completes the main result.