Does there exist a constant c>0 such that, for all sufficiently large integers n and every polynomial P∈ C[z] satisfying P.operatornamenatDegree=n and, for every i≤operatornamenatDegree(P), [z^i]P∈-1,1, one has sup_|z|=1|P(z)|>(1+c)√ n?

RemarkAI-assistedClaimed by OpenAI. The manuscript claims that the least possible unit-circle maximum of a real-sign polynomial with N terms is (1+o(1))*sqrt(N) through all integer lengths. This contradicts the target’s proposed universal fixed positive gap above sqrt(degree). The manuscript also deduces unbounded binary merit factor; this manuscript alone does not claim two-sided ultraflatness.See full solutionHide full solution

Claimed by OpenAI. The manuscript claims that the least possible unit-circle maximum of a real-sign polynomial with N terms is (1+o(1))*sqrt(N) through all integer lengths. This contradicts the target’s proposed universal fixed positive gap above sqrt(degree). The manuscript also deduces unbounded binary merit factor; this manuscript alone does not claim two-sided ultraflatness.

GitHub repository: https://github.com/openai/math

Manuscript: https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Asymptotically-minimal-maxima-of-real-Littlewood-polynomials-September-23-2026/paper.pdf

OpenAI-076-03-Asymptotically-minimal-maxima-of-real-Littlewood-polynomials.pdf483,466 bytesOpen