= Hypergraph container theorem
For fixed uniformity, sufficiently small nonsingleton <hypergraph codegrees> relative to $d\tau^{|\sigma|-1}$ permit a family of containers whose degree measures are bounded below one by a fixed amount. Each container has a <container fingerprint> of size $O(\tau n)$. Iteration gives containers inducing at most an arbitrary fixed proportion of all hyperedges, with logarithmic family size $O(n\tau\log(1/\tau))$. The constants depend on the uniformity and desired edge proportion, and the average degree must be positive.
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