Golay’s merit factor conjecture

Establish a uniform bound on the merit factor of Littlewood polynomials, i.e., prove that the quantity C_golay^4(n) remains bounded by an absolute constant for all degrees n.

Background

Golay’s merit factor measures fourth-moment deviation from L2 energy for sequences/polynomials with ±1 coefficients. Heuristics and numerical evidence suggest bounded behavior, but a proof is lacking.

Uniform control would have ramifications for sequence design, coding theory, and analytic number theory related to autocorrelation.

References

Golay's merit factor conjecture asserts the uniform bound $$ C_{\ref{golay}4(n) \lesssim 1. $$

— Mathematical exploration and discovery at scale  (2511.02864 - Georgiev et al., 3 Nov 2025) in Subsection “Flat polynomials and Golay’s merit factor conjecture” (Section 4.16)