= Strong regularity for three-uniform hypergraphs
= Strong hypergraph regularity
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Strong regularity refines both the vertex classes and the pair graphs supporting triple hyperedges. The resulting <triads in a hypergraph regularity partition> have nearly constant relative triple density outside a small exceptional weight. Pair and triple errors must be chosen in a hierarchy strong enough for a relative <tetrahedron counting lemma>; ordinary graph regularity on the vertex partition alone is insufficient. Refinement raises bounded conditional-density energies.
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