Deciding whether an arbitrary integer polynomial in subset densities and additive energies is nonnegative for all subsets of all finite abelian groups is undecidable.
Additive energy and the metric poissonian property
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Undecidability of Polynomial Inequalities in Subset Densities and Additive Energies
Deciding whether an arbitrary integer polynomial in subset densities and additive energies is nonnegative for all subsets of all finite abelian groups is undecidable.