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Claim. The answer to both questions of Problem 92 is no. Theorem 1.1 of the report Planar Point Sets with Many Unit Distances, authored by OpenAI and attributed by the report to an internal OpenAI model, gives an absolute constant $\delta>0$ and infinitely many $N$ with an $N$-point planar set carrying at least $N^{1+\delta}$ unordered pairs at Euclidean distance one. The paragraph after the theorem turns to the stronger conjecture of Erdős and Fishburn [ErFi97], point sets in which every point has at least $k$ equidistant neighbors, at a distance that may depend on the point, and states that the theorem refutes the predicted bound $k\le n^{o(1)}$: along the sequence the unit-distance graph has average degree $N^{\Omega(1)}$, and a graph of average degree at least $2k$ contains a subgraph of minimum degree at least $k$. Spelled out, deleting vertices of degree below $N^\delta$ one at a time cannot exhaust the graph, since that would count fewer than $N^{1+\delta}$ edges; the surviving $m$ points have minimum degree at least $N^\delta\ge m^\delta$, with $m\ge N^\delta+1$ unbounded, so each of them has at least $m^\delta$ other survivors at distance one and $f(m)\ge m^\delta$ along an unbounded sequence. A fixed power exceeds $m^{o(1)}$ and $m^{C/\log\log m}$ for every fixed $C$ once $m$ is large, so both the bound $f(n)\le n^{o(1)}$ and the stronger $f(n)<n^{O(1/\log\log n)}$ fail. The report does not name the problem by its number. It is carded at openai_2026_planar_point_sets_many_unit_distances and the theorem, with the transfer written out, is paged at Theorem 1.1. The report's PDF metadata gives a creation date of 19 May 2026 and the site's pages crediting the result were edited on 20 and 21 May 2026, so the posting is dated 20 May 2026 here, as on the Problem 90 page.

Depends on. OpenAI's accepted claim on Problem 90 supplies Theorem 1.1, the fixed-power unit-distance sets; the pruning step is elementary and is stated in the report.

Acceptance. The reviewed evidence is the one recorded for Theorem 1.1 on the Problem 90 page: the check of the model's proof documented in the companion manuscript Remarks on the disproof of the unit distance conjecture, arXiv:2605.20695v1, by nine mathematicians, none an author of the report, whose Section 6, written by Daniel Litt, records that Litt was asked by OpenAI to check the solution's correctness and became convinced that it is correct. Beside it, the site's curator, Thomas Bloom, marks this problem disproved and states on its page that the disproof of Problem 90 also disproves this stronger form (problem page last edited 21 May 2026); the curator is a coauthor of the companion manuscript, which does not itself state the Problem 92 consequence, so the curator's label covers the transfer and the check Litt documents in the companion manuscript covers the theorem it rests on. The corpus's own retained full review of the reconstructed chain, which includes this transfer, counts for nothing here. No journal publication or arXiv version of the report is known, and the Lean developments recorded on the Problem 90 page formalize that problem's statement, not this one's, so no formalization is linked.

Other postings of the same deduction. A comment on the site's discussion thread of 20 May 2026 reproduced the pruning deduction, generated with GPT-5.5 Pro, and a reply located the same deduction in the report; a thread post is not a dated manuscript and gets no page. The companion manuscript, on its Problem 90 page, and Sawin's explicit construction, on Sawin's page, each give fixed-power unit-distance sets from which the same pruning yields the same conclusion, but neither manuscript states it; the transfers from them recorded on the library pages and on the problem page are the corpus's own deductions and give no claim page.