Claims

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2016_09_12_el_abdalaoui: A 2016 preprint claims that no sequence of plus or minus one polynomials is square L^2-flat, that is L^4-flat, so Erdős's ultraflat conjecture holds; rejected after the accepted disproof.

2025_04_30_el_abdalaoui: A 2025 preprint claims that plus or minus one polynomials are never L^alpha flat for even alpha above two, which would give the universal gap asked for; rejected after objections in the site's thread and the accepted disproof.

2025_09_04_el_abdalaoui: A September 2025 preprint claims that plus or minus one polynomials are not L^alpha-flat for any alpha > 0, so their maximum modulus exceeds (1+d) times the square root of n; rejected after the accepted disproof.

2026_09_23_openai: Theorem 1.1 of the OpenAI release manuscript of 23 September 2026: for every positive eta and every large N some signs give a polynomial of maximum modulus at most (1+eta) times the square root of N, so the answer is no.

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