Iterative calculation values in the Collatz conjecture eventually reach 1 as if walking across tightropes

I attempt to verify the Collatz conjecture. Through careful examination, I find that the evolution of the iterated values before reaching 1 can be characterized by four types of operations. Two dynamical models are constructed to demonstrate that the values necessarily decrease. However, these models do not explain the mechanism by which the value ultimately reaches 1. To address this limitation, I introduce a mathematical framework termed the Collatz rope model, in which each rope consists of an odd terminal value together with the even numbers generated by multiplying that value by powers of two. Within this framework, I derive a criterion that determines whether the final value becomes 1, and I show that all iterative sequences satisfy this criterion. Furthermore, it is established that the iterated values cannot diverge to infinity. Taken together, these results lead me to conclude that the Collatz conjecture holds for all natural numbers. I am currently publishing explanatory videos on my YouTube channel that describe and expand upon the content presented in these two papers. All related videos are collected in the playlist available at the following link: https://www.youtube.com/playlist?list=PLJqPJWRhQcY7q2IWhcsza0_KhgZGX6C21 By subscribing to my channel, you will receive notifications when new videos are released.