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Claim. The preprint el Houcein el Abdalaoui, A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$, arXiv:2509.04212 (one version, posted 2025-09-04), states as Theorem 1 a weighted criterion: no sequence of analytic polynomials $P_n(z)=\sum_{m=1}^nc_mz^m$ with $\sum_m\lvert c_m\rvert^2\le Kn^{-2}\sum_m m^2\lvert c_m\rvert^2$, for an absolute constant $K$, is $L^\alpha$-flat for any $\alpha>0$. Its Corollary 3 states that sequences of $\pm1$ polynomials are not $L^\alpha$-flat for any $\alpha>0$, and its introduction deduces $\lVert P\rVert_\infty\ge(1+d)\sqrt n$ for every normalized $\pm1$ polynomial, which is Problem 1150 answered yes. The preprint presents this as generalizing the author's April 2025 claim (el Abdalaoui 2025).

Depends on. No page of this wiki for the claim itself; the rejection below rests on the accepted OpenAI 2026 page.

Rejection. The accepted Theorem 1.1 of the OpenAI release contradicts the bound directly: for every $\eta>0$ and every large $N$ it gives signs with $\max_{\lvert z\rvert=1}\lvert P(z)\rvert\le(1+\eta)\sqrt N$. Appendix A.2 of the release manuscript (card) shows Theorem 1 false for weighted coefficients, and shows the signed-modulus identity used for Corollary 3 false ($P(z)=1+z$, $z=1$, $z'=i$). Not reviewed; not refereed.