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Submission note. Posted to erdosproblems.com as a proof claim by Lucas Ewing (account luew2) on 28 August 2026, giving "GPT 5.6" as the AI used:

Upped to 7 primitives

The claim. Published on 27 August 2026 in the submitter's repository erdos-488-size-7-candidate, the date that names this page, and submitted to the proof-claim tab of Problem 488 on 2026-08-28 by Lucas Ewing as a partial proof claim made with GPT 5.6, the system the tab names, with a one-line summary saying that the proof now reaches seven primitive elements: a computer-assisted candidate proof that the site's doubling inequality holds when the primitive reduction of $A$, its elements divisible by no other element, has at most seven members. The manuscript is linked at the repository's commit of 27 August 2026; the exact hypotheses and the form of the computer assistance are those the submission states.

Covers. The site's inequality for sets $A$ with at most seven primitive elements, as the submission describes its scope; it says nothing about larger primitive reductions.

Standing. Claimed. The site has not commented on the submission, the tab entry has no comments, and no outside review was found on 2026-09-18 or 2026-10-07. The restriction is consistent with the counterexample claim of 5 September 2026, whose set has far more than seven primitive elements. The earlier partial claim of Chojecki covers primitive reductions of size at most three, so this claim extends that range to seven; the later partial claim, the excess-fifteen bound, restricts the excess of the primitive reduction rather than its size, and neither claim is stated in terms of the other. The thread's other positive results for restricted classes of $A$ (two-element sets, primitive sets containing $2$, sets of primes in the limit) are forum comments recorded on the problem page, not proof-claim submissions.

Depends on. Nothing in this wiki: the claim rests on its own manuscript.