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OpenAI · 147-02 · 2026-09-24 · Dynamical systems and ergodic theory

Rigidity of Smooth Billiards with a Continuous Caustic Collar

preprints/Rigidity-of-Smooth-Billiards-with-a-Continuous-Caustic-Collar-September-24-2026

Family 147. The near-boundary Birkhoff conjecture.

The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.

Read against the standing problems

Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N

Resolves the near-boundary Birkhoff conjecture for smooth strictly convex planar billiards of positive curvature. Such a billiard is an ellipse whenever a full grazing annulus is continuously foliated by individually invariant essential curves. A continuous physical collar of smooth closed convex caustics also suffices.

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.

Preprint source and Lean scope

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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.