Restriction conjecture

Common card · No. 474611

In harmonic analysis, the restriction conjecture, also known as the Fourier restriction conjecture, is a conjecture about the behaviour of the Fourier transform on curved hypersurfaces. It was first hypothesized by Elias Stein. The conjecture states that two necessary conditions needed to solve a problem known as the restriction problem in that scenario are also sufficient. The restriction conjecture is closely related to the Kakeya conjecture, Bochner-Riesz conjecture and the local smoothing conjecture. On October 26, 2026, OpenAI made an announcement claiming to have proved the local smoothing conjecture, and thus the restriction conjecture by implication. As of October 26, 2026, the claim has not been peer reviewed.

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