Harmonic analysis

Check the benchmark version, sampling budget, data contamination controls, human interventions and proof-review method. A final answer or benchmark score is not evidence that every reasoning step is valid.

Explained dossiers

01OpenAI2026-10-26

Local smoothing ⇒ Kakeya + restriction

Local smoothing, Kakeya and restriction

Imagine moving a very thin needle in every direction while using almost no space. The Kakeya conjecture asks how small such a set can be. An OpenAI system reports a route to resolving this and related questions about waves.

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Harmonic analysis

Explained dossiers

Local smoothing, Kakeya and restriction

Research notes