Preliminary Exploration of Solving Collatz via Identity Transformation

Starting from the connection between the Collatz conjecture and Diophantine equations, we conduct an in-depth analysis of their underlying equation structures and construct a multiple Diophantine equation model with 4 as the dominant parameter and 2 as a fine-tuning parameter. Within this framework, the Collatz iteration process is interpreted as the recombination and redistribution of coefficients. By employing an equation system centered on 4 with 2 as a corrective term, we investigate the existence of solutions for the sequences and the patterns of numerical redistribution. Furthermore, by introducing the concept of remainder allocation, we can further uncover the mechanisms behind value redistribution, thereby providing a novel theoretical framework for analyzing the Collatz conjecture.By constructing a novel identity-based dynamical system, we establish a new paradigm for addressing this problem.(This work was developed in spare time, resulting in slow progress and relatively frequent errors. This article is currently incomplete)