Finite Reduction of the Collatz Conjecture via Mean Contraction and Diophantine Cycle Classification

This preprint presents a structural result on the Collatz conjecture. Rather than claiming a complete proof, the work demonstrates that the conjecture can be reduced to the non-existence of non-trivial cycles within an explicitly bounded finite set. The reduction is achieved by combining a mean contraction argument based on a Lyapunov function with a Diophantine classification of all possible cycles. As a consequence, the problem is shown to be equivalent to a finite, explicit, and decidable verification. The final computational execution of this verification is left as an independent subsequent step.