Deciding whether an arbitrary integer polynomial in subset densities and additive energies is nonnegative for all subsets of all finite abelian groups is undecidable.
Undecidability of polynomial inequalities in weighted graph homomorphism densities
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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.