A Complete Proof of the Collatz Conjecture

This preprint presents a complete and elementary proof of the Collatz Conjecture. The work eliminates the possibility of nontrivial cycles by formal derivation of the general cycle formula, and proves convergence to the trivial cycle {1, 2, 4} via a recursive inversion method. The result was independently developed by the author and is intended to serve as a public record of priority and to invite formal verification and commentary.