Unbounded improvement over Erdős’s N/3 lower bound for S(N)
Determine whether there exists a function ω(N) that diverges to infinity such that S(N) ≥ N/3 + ω(N), i.e., establish an unbounded additive improvement over Erdős’s N/3 lower bound.
References
Is there a function $\omega(N)\to\infty$ such that $S(N)\geqslant \frac{N}{3}+\omega(N)$?
— Large sum-free subsets of sets of integers via $L^1$-estimates for trigonometric series
(Bedert, 12 Feb 2025) in Section 1 (Introduction), Problem \ref{conj:sumfree}