Problem 510: Positive differences and the square-root scale

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positive_difference_normalization: An exact cosine identity for positive differences, with the factor two retained, supplies small-excursion examples at every cardinality but no universal lower bound.

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The [[research/erdos_510/positive_difference_normalization|argument on positive differences and the square-root scale]] records its exact scope, source premises, and remaining gap toward [[problems/analysis/E0510/_index|Problem 510]].