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OpenAI, Ten Advances in Mathematics and Theoretical Computer Science, technical report announced 1 August 2026 with its original PDF (the claim's date; linked above), PDF revised 6 August 2026, the version cited; Chapter 10, Counterexamples to the Compactness and Degeneracy Conjectures for Extremal Numbers, Theorem 1.2, printed pp. 237--238. The report's author is OpenAI; its announcement attributes the arguments to an internal model and the manuscript's preparation to humans working with that model, and the chapter names no individual author. Library pages: the card and the result page.

The result. A graph is $r$-degenerate when every nonempty subgraph has a vertex of degree at most $r$, the form equivalent to the problem's induced-subgraph wording. Theorem 1.2: there exist a fixed connected bipartite $2$-degenerate graph $H$ and constants $c,\varepsilon>0$ with

$$\mathrm{ex}(n,H)\ge c\,n^{3/2+\varepsilon}$$

for all sufficiently large $n$. The problem asserts $\mathrm{ex}(n;H)\ll n^{2-1/r}$ for every $r$ and every bipartite $r$-degenerate $H$; at $r=2$ the asserted bound is $O(n^{3/2})$, which $c\,n^{3/2+\varepsilon}$ exceeds for large $n$, so the universal statement fails at the pair $(2,H)$ and the problem is disproved. The graph is built in layers: $V_0$ of size $L_0$, $V_i=\binom{V_{i-1}}2$, each vertex $\{a,b\}\in V_i$ joined to its two parents; the lower bound comes from a random induced subgraph of a bipartite Hamming-ball graph, which Proposition 8.1 shows is $H$-free by an entropy-potential argument, with a second-moment edge count and padding giving $c=2^{-3/2-\varepsilon}$ (pp. 247--248). The problem page's Current assessment records the reading depth: statements and the construction were checked clause by clause, the proof was read for structure only, and no step was checked.

Depends on. Nothing in this wiki; the argument is self-contained within the chapter, and the problem page's account rests on this claim.

Acceptance. Reviewed: the site's curator, Thomas Bloom, labels the problem DISPROVED (LEAN) and wrote the commentary crediting the disproof to an internal model at OpenAI, with the connected bipartite $2$-degenerate $H$ and the exponent $3/2+c$ (erdosproblems.com/146, accessed 2026-09-18; the page was last edited 31 August 2026, and the community database lists the status disproved (Lean) as of its last update, dated 2 August 2026, without recording when the state changed, so the day of the relabel itself is not established); Bloom took no part in the report. That documented acceptance by the site is the only acceptance evidence: no refereed publication, no arXiv version and no written independent expert review of the argument were found on 2026-09-18 (the problem page's search scope), so the standing rests on the site's acceptance of an AI-generated argument, and nothing is independently reviewed in this repository. A refereed version, an independent whole-argument review or a build of the formal proof checked against the problem's statement would add evidence.

Formalization, not evidence. The file CompactnessAndDegeneracy.lean of openai/ten-proofs at the pinned commit (linked above) proves not_erdos_146 against its own DegeneracyConjectureStatement, and the formal-conjectures statement file recorded on the problem page points to it through a formal_proof attribute. The file contains no sorry, axiom or native_decide, the corpus has not built or audited it, and the two files' degeneracy definitions were not bridged, so it is listed as a link and not as formalized evidence.