Littlewood polynomial flatness

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idempotent_concentration_audit: The 2025 concentration argument uses the wrong quantifier; its concluding concentration holds under a fixed norm bound.

source_notes/: Paper summaries and source comparisons used in the research on Problem 1150.

source_proof_audit: Checked failures in claimed flatness proofs and a Barker reflection formula, including an explicit counterexample to a separate 2025 criterion; no resolution of the main problem.

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Where things stand

Disproved. For length $N=n+1$, the OpenAI release's construction (claim page) gives, for every $\eta>0$ and every large $N$, Littlewood polynomials with $\|P\|_\infty\le(1+\eta)\sqrt N$, so no uniform gap exists. The source audits and concentration audit leave no other supplied claimed resolution certified. The source notes summarize the literature used here.