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Claim. The preprint el Houcein el Abdalaoui, On the Erdős flat polynomials problem, Chowla conjecture and Riemann Hypothesis, arXiv:1609.03435 (v1 2016-09-12; v2 2017-01-11, adding "Chowla conjecture and Riemann Hypothesis" to the title), states as Theorem 3.3 of v2 that no sequence of normalized $\pm1$ polynomials is square-$L^2$-flat; its definition (2.1) fixes the first and last coefficients to $+1$. It deduces that Erdős's $L^4$ and ultraflat conjectures hold. Since $\lVert\,\lvert P\rvert^2/N-1\rVert_2^2=\lVert P\rVert_4^4/N^2-1$ for a $\pm1$ polynomial $P$ of length $N$, square-$L^2$ flatness is $L^4$ flatness, and the claim is the case $\alpha=4$ of the author's 2025 claim (el Abdalaoui 2025). With $\max_{\lvert z\rvert=1}\lvert P(z)\rvert\ge\lVert P\rVert_4$, it would answer Problem 1150 yes.

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 gives, for every $\eta>0$ and every large $N$, signs with $\lVert P\rVert_4^4\le\max_{\lvert z\rvert=1}\lvert P(z)\rvert^2\lVert P\rVert_2^2\le(1+\eta)^2N^2$, so its polynomials are square-$L^2$-flat. Appendix A of the release manuscript (card) notes that changing at most two endpoint signs costs at most $4/\sqrt N$ in normalized uniform norm, so the conclusion fails in the preprint's convention too. Not reviewed; not refereed, and no journal version is known.