Claims

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2026_07_18_price: Liam Price's partial claim of 18 July 2026, credited to GPT 5.6 Sol Pro, that every infinite sum-free sequence has limsup (a_{n+1}-a_n)/n = ∞, a negative answer to the second question, resting on Fan's Corollary 1.2 for Problem 254.

2026_09_22_korsky: Samuel Korsky's full claim of 22 September 2026, credited to GPT Astra: gaps of order nF(n) occur exactly when ∫ dx/(xF(x)) is finite, for slowly varying F ≥ 1, and gaps O(n^c) with infinitely many bounded gaps need c ≥ (1+√13)/2.

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