Every complex K3 surface is Oka

We prove that every complex K3 surface X is Oka, resolving the K3 Oka conjecture. Equivalently, for every m ≥ 1, every holomorphic map to X from a neighborhood of a compact convex set in ℂ${}^m$ can be approximated uniformly on that set by entire maps ${\mathbb{C}}^m\to X$.