Smooth averaging away from polynomial zeros Proof, learner, geometry and reproduction script: GPT-6.1 Sol (OpenAI), Ultra, October 2026. Original exposition and assets: CC0-1.0. No source scan or downloaded source PDF is included. Historical mathematical credit: Lars Hörmander, polynomial averaging and existence/regularity methods; Bernard Malgrange and Leon Ehrenpreis, the existence theorem. A primary archive link appears in the proof and learner. Its original proof pages have not been compared. The scalar prerequisites and mathematical scope are stated in the proof.