Remark: Family 076. Ultraflat real Littlewood polynomials

Constructs polynomials with $N$ consecutive coefficients in $\{-1,1\}$ whose modulus is $(1+o(1))\sqrt{N}$ uniformly on the entire unit circle, for every sufficiently large integer length $N$. Thus real Littlewood polynomials are ultraflat, including at the real endpoints. Their binary merit factors tend to infinity, disproving Turyn's bounded-merit-factor conjecture.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.