Open. The site labels the problem OPEN (page last edited 3 December 2025). Its commentary credits two bounds. Konyagin's 2004 bound on the finite analogue, Problem 1109, gives $a_j\ge j^{15/11-o(1)}$ for every infinite set with squarefree sums, recorded on Konyagin 2004. Van Doorn and Tao's first arXiv version (30 November 2025) proves $a_j>0.24\,j^{4/3}$ for all $j$ and constructs a squarefree such set with $a_j\le\exp(Cj/\log j)$, recorded on van Doorn and Tao 2025. The site's proof-claims tab carries a partial proof claim by Xiyu Hu, submitted on 23 July 2026 under the username hxypqr with GPT-5.6 Sol named as assistance: an infinite set with squarefree pairwise sums, doubles included, and $|A\cap[1,x]|\gg(\log x)^2$, so that $a_j\le\exp(C\sqrt j)$, built from van Doorn and Tao's extension method and Konyagin's quadratic Brun sieve, with a partial Lean 4 development; it is recorded on its claim page (Hu, 2026). The claim concerns the construction side only and has no acceptance evidence.