A Proof of the Axion?

We show that the de Sitter quantum breaking bound when applied to QCD exposes the necessity of the axion solution to the strong CP problem. The Peccei-Quinn mechanism emerges as a consistency requirement independent of the naturalness questions. The $\theta$-angle must be unphysical rather than simply small. All other approaches including a fine-tuning of $\theta$ lead to the existence of de Sitter vacua and are excluded by consistency.