Problem 256: Distinct exponent products at every cardinality

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distinct_exponent_cardinality_extension: Integer dilations combine Bourgain–Chang dense blocks into every prescribed cardinality with the same logarithmic norm order, without a linear frequency bound.

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The [[research/erdos_256/distinct_exponent_cardinality_extension|argument on distinct exponent products at every cardinality]] records its exact scope, source premises, and remaining gap toward Problem 256.