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Claim. Przemek Chojecki's post of 21 April 2026 in the discussion thread of Problem 584 links the five-page note A note on the formulation of Erdős Problem #584, dated 21 April 2026 and naming no author in its text, and credits its counterexample to GPT-5.4 Pro. The note's Theorem 1 derives from the graphs $CD(5,q)$ of Lazebnik, Ustimenko and Woldar, $q$-regular of girth at least $10$ on at most $2q^5$ vertices, infinitely many $n$-vertex graphs with at least $2^{-6/5}n^{6/5}$ edges and girth at least $10$. Its Corollary 2 observes that such a graph has $\delta\ge2^{-6/5}n^{-4/5}$, so $\delta^2n^2\to\infty$, while a subgraph in which every two edges lie on a cycle of length at most $8$ has only one edge; so the second clause fails as written when $\delta$ is left unrestricted, and, by deleting edges, for every $\delta=n^{-\beta}$ with $4/5<\beta<1$. Its Remark 3 says this leaves the sparse problem with $\delta\ge n^{-\beta_0}$ untouched, and its Proposition 4 re-proves the $\delta^3$ weak $C_6$ core, which the note credits to Duke, Erdős and Rödl.

Submission note. Posted to the erdosproblems.com forum by Przemek Chojecki on 21 April 2026:

Looks like GPT-5.4 Pro can construct a counterexample to the second statement if there's no additional conditions on sparsity. Have a look here for discussion and references.

Why it is rejected. It answers a variant, not the Statement. The note refutes the second clause read uniformly over all $\delta$, with absolute implied constants and no condition on how small $\delta$ may be. Problem 584 adopts, as its Formulation states, the question the erdosproblems.com commentary singles out: whether some $c>0$ makes both clauses hold, with absolute implied constants, for $\delta=n^{-c}$ and all large $n$. A failure confined to $4/5<\beta<1$ excludes no $c\le4/5$, and the second clause is already known for every $c<1/5$, so its mathematics answers the variant and does not settle this problem; the value disproved is its answer to that variant.

Standing. Rejected, as answering a variant. A reply of the same day by another account, linking a chat transcript, reports that an automated check found two minor issues in Proposition 4 that do not affect Theorem 1; that is a thread comment, not a review. The note is unrefereed and reviewed by no named mathematician on the thread, and this corpus has not checked its proof. The failure it gives is the one Fox and Sudakov's remark on p. 1061 of their 2008 paper gives through Benson's graphs, here with an explicit range.

Depends on. No page of this wiki.