Robust ladders in the HLM tower construction for arithmetic regularity over ${\bf F}_2^{\,n}$

Green's arithmetic regularity lemma over $G={\bf F}_2^{\,n}$ has tower-type lower bounds. We show that the order property in the Hosseini--Lovett--Moshkovitz--Shapira construction is robust under adversarial edits. Write $f=s^{-1}\sum_{i=1}^{s}\mathbf 1_{A_i}$, where $s=\lfloor1/(16ε)\rfloor$, and l