{"id":"openai-math/Rigidity-of-Smooth-Billiards-with-a-Continuous-Caustic-Collar","pdf":"https://github.com/openai/math/blob/main/preprints/Rigidity-of-Smooth-Billiards-with-a-Continuous-Caustic-Collar-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Rigidity-of-Smooth-Billiards-with-a-Continuous-Caustic-Collar-September-24-2026","tags":["billiards","dynamical-systems","birkhoff-conjecture"],"score":0,"title":"Rigidity of Smooth Billiards with a Continuous Caustic Collar","domain":"Dynamical systems and ergodic theory","family":"147","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DS","summary":"We prove that a smooth strictly convex planar billiard with positive curvature is an ellipse whenever a full neighborhood of its boundary is continuously foliated by smooth closed convex caustics. No differentiability across the leaves is assumed. This resolves the near-boundary Birkhoff conjecture in the stated smooth class.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"The near-boundary Birkhoff conjecture"}