Root Jumps Over k Values in the Collatz Equation

Although the aim of this text is to show that there are no loops other than 1, numerous shortcuts have been found on the way to the main goal, and Collatz branches have been reduced from massive systems to small groups. The function of this depends on how one views its benefits. It can be seen as a way to reduce CPU load on a system. It can be seen as a way to minimize a Collatz system. Classical mathematicians will look for this and say, "This 4 2 1 loop doesn't explain the existence of a loop other than 1. The article is insufficient."