Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 147-02. Rigidity of Smooth Billiards with a Continuous Caustic Collar
Manuscript map · lines 5235–5244
OpenAI@2026-10-07#rem:oai-p-147-02
Authors: OpenAI. Family 147.
Title: Rigidity of Smooth Billiards with a Continuous Caustic Collar.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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