A Dual-Layer Approach to the Collatz Conjecture: Classical Algebra and Functional Symmetry

The Collatz Conjecture, also known as the 3n + 1 problem, remains one of the most enigmatic questions in number theory. This document presents a dual-layered approach for exploring its structure and behavior: first using classical algebraic transformations, and then reinforcing the insight through functional sequence symmetry. [1]The author acknowledges the use of OpenAI’s language model for assistance in drafting certain sections of this work.