Collatz Conjecture Proof

This paper presents a deterministic proof of the Collatz Conjecture, demonstrating that every positive integer converges to 1 under the standard Collatz iteration. By leveraging the 2-adic valuation v2(3n+1)v_2(3n+1)v2(3n+1) and analyzing the dynamics of the Syracuse function, we establish a universal logarithmic contraction. Key results include bounding the average valuation per odd step and rigorously excluding non-trivial cycles and divergence. Supported by simulations up to 10 to power 10, this work offers a resolution to a long-standing problem and highlights the power of valuation-based methods in dynamic number theory.