(k+1)-uniform hypergraphs definable in NIP strongly k-distal structures admit homogeneous regularity lemmas whose partitions are uniformly definable and polynomially bounded in 1/δ.
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Homogeneous hypergraph regularity lemmas via $k$-strong honest definitions
(k+1)-uniform hypergraphs definable in NIP strongly k-distal structures admit homogeneous regularity lemmas whose partitions are uniformly definable and polynomially bounded in 1/δ.