Claims

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2026_05_16_liu: A note of 2026-05-16 by Yu Leon Liu claimed a full proof that the mean squared sumset gap of Sidon sets tends to infinity; its one input, a shifted-intersection bound, was retracted the same day and the note withdrawn.

2026_05_19_liu: A note of May 2026 by Yu Leon Liu proves that the mean squared sumset gap tends to infinity along every sequence of Sidon sets whose diameter is (1 + o(1)) n squared, through Pikhurko's uniformity lemma; unexamined.

2026_08_14_kapoor: A write-up of August 2026 bounds the mean squared sumset gap of a Sidon set below by a constant times the smaller of log n and log 1/(kappa - 1), kappa the diameter over n squared; sets of nearly minimal diameter answer yes.

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