Open. The site's label is OPEN (page last edited 4 November 2025). Its proof-claim tab carries one partial claim, submitted 2026-08-20 by the forum account DottedCalculator, the claimant, with a five-page write-up signed by the AI system GPT 5.6 Sol: for every large $k$, every even number up to a constant times $p_k$ is a difference $a_{i+1}-a_i$, so the smallest even integer that is not such a difference is $\gg p_k\sim k\log k$ and $\gg p_k$ distinct even differences occur; the write-up says that it does not settle the displayed comparison with $\max_i(a_{i+1}-a_i)$. The claim is recorded on its claim page (DottedCalculator, 2026) without adoption: no comment, review or outside record was found, and nothing is reviewed here. The write-up names two earlier public lower bounds, each recorded as a claimed partial result: Ziller's 2020 preprint shows that $2,4,\ldots,2k$ all occur as differences, and White's working report of 27 July 2026, written with Claude, proves that the smallest even non-difference is at least $(e^{\gamma}-o(1))k\log\log k$. A partial claim leaves the standing open.