A moment identity over homomorphisms yields candidate low-soundness tests for cyclic, automorphism, and Lie settings, but one headline theorem is stated with an impossible guarantee.
On the Bogolyubov-Ruzsa lemma
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abstract
Our main result is that if A is a finite subset of an abelian group with |A+A| < K|A|, then 2A-2A contains an O(log^{O(1)} K)-dimensional coset progression M of size at least exp(-O(log^{O(1)} K))|A|.
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A General Framework for Low Soundness Homomorphism Testing
A moment identity over homomorphisms yields candidate low-soundness tests for cyclic, automorphism, and Lie settings, but one headline theorem is stated with an impossible guarantee.