Sidorenko property for affine-type binary configurations

Prove or disprove that every affine-type linear configuration in F_2^n is Sidorenko, equivalently that every affine-type simple system of linear equations over F_2 is Sidorenko.

Background

The Sidorenko property requires every host configuration of density α to contain at least the random-model number of homomorphisms, or equivalently yields a corresponding supersaturation statement. The authors identify a complete conjectural characterization over F_2 in the affine-type case.

References

Every affine-type linear configuration in $\mathbb F_2n$ is Sidorenko. Equivalently, every affine-type, simple system of linear equations over $\mathbb F_2$ is Sidorenko.

— Generic solutions to symmetric linear equations  (2610.02177 - Frederickson et al., 1 Oct 2026) in Conjecture, Section 1, subsection “Systems of linear equations”