Functions built from intersections of set families satisfy a strong hypergraph regularity lemma, and the two known sources of ternary instability both satisfy this regularity, so strong 2-stability cannot be defined by excluded hypergraphs.
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Averages of hypergraphs and higher arity stability
Functions built from intersections of set families satisfy a strong hypergraph regularity lemma, and the two known sources of ternary instability both satisfy this regularity, so strong 2-stability cannot be defined by excluded hypergraphs.