Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Claim. Let be the extremal function of Problem 302, the largest size of a set with no three distinct elements satisfying . The linked text states
Its route, as it describes it: a five-element configuration carrying three solutions is embedded in a tile of integers of the form (excluding ); the omissions that a solution-free set must make from are catalogued at nine thresholds; the dilates for with are pairwise disjoint, and such have density ; summing the forced omissions over the dilates gives the bound. The text compares its constant with , which it calls the previously applicable bound: the site's argument for Problem 301 uses only the three two-term relations inside and so holds for this problem too; the claimed constant would improve both it and the the site records here.
Covers. An upper bound for the estimate of . It does not bear on the particular question, which Cambie's construction answers in the negative, and it bounds above by without determining the constant.
Standing. Claimed. The claim was filed as partial on the site's proof-claim tab on 20 July 2026 by the account 15Redstones; the tab credits it to Robert Schuh and names the systems GPT 5.6 and Kimi 2.6, and the claimant is the human named there. The tab gives no summary, and the only link is a text on a paste site that is undated, unsigned and silent about how it was written; it has no arXiv version, no journal record, no formalization and no independent review, and no comment stands under the claim. Nothing was checked here beyond reading the statement. The site's label is OPEN, and the tab's standing notice says that listing a claim implies no examination.