<b>Demonstration of the Uniqueness of the Loop in Collatz Sequences Based on Digital Roots and Graph Theory.</b>

This study demonstrates that the loop 4, 2, 1, 4 is the only possible loop in Collatz sequences, using adetailed analysis of the digital roots of the numbers involved and modeling the system as a directedgraph. Through this approach, it is shown that the mathematical properties of digital roots and therules of the Collatz conjecture make the existence of other loops impossible. It is concluded that,based on this analysis, no other loops can exist in Collatz sequences.