A Functional Approach to the Collatz Conjecture

The Collatz Conjecture, also known as the (3n+1) problem, is a longstanding unsolved problem in number theory. This paper explores a functional and logarithmic measure approach to the conjecture, combining Python-based experimentation, lambda calculus formulation, and log-space analysis. We formalize the sequence using functions and analyze their behavior using a measure function. While a complete proof is not yet established, this framework provides a structured pathway for reasoning about convergence for all positive integers.