Preprint in the OpenAI Math release
The circulant Hadamard conjecture
OpenAI
Abstract
We prove the circulant Hadamard conjecture: a real circulant Hadamard matrix has order 1 or 4. As a consequence, Barker sequences of length greater than one exist exactly at lengths 2, 3, 4, 5, 7, 11, 13, proving the Barker-sequence conjecture.
open until 1 Jan 2028
est. 50% chance this result is independently verified by the end of 2027.
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