Determine S(N), the minimum guaranteed size of a largest sum-free subset
Determine the exact value or sharp asymptotics of S(N), defined as the minimum over all sets A of N positive integers of the size of the largest sum-free subset S(A).
References
One of the most central open questions in this area is that of determining the quantity $S(N)$ which is defined to be the largest integer $S$ such that any set of $N$ positive integers contains a sum-free subset of size $S$.
— Large sum-free subsets of sets of integers via $L^1$-estimates for trigonometric series
(Bedert, 12 Feb 2025) in Section 1 (Introduction)