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.

翻译：Collatz假设是自然数算法理论中的一个定理。我们证明了表达Collatz算法停机性质的（算法）公式。观察到Collatz定理在任何初等数论中都无法被证明，这完成了主要结果。