Resolves the Burr–Erdős hypercube Ramsey conjecture: the two-color Ramsey number of the n-dimensional cube is \(\Theta(2^n)\). Thus every red-blue coloring of a complete graph on a universal constant times the cube’s number of vertices contains a monochromatic copy of the cube.
The release has no Lean statement for this family, so there is no formal statement to compare with the result described above.
It bears on Erdős problem #181, as listed by Thomas Bloom, erdosproblems.com.
The paper states
In The hypercube Ramsey number has linear order, 23 September 2026
Possible match to OpenAI’s description, selected from shared wording. No review confirming the selection is recorded.
There is an absolute constant C>0 such that
The release does not say which paper theorem its catalogue describes. The statement above shares the most wording with the description; the atlas has not reviewed that choice. Identifying it is listed under Questions awaiting review.
Each paper opens as a reading page in the browser, with the PDF beside it. The statements each paper opens with are on its reading page.
The release has no Lean statement for this family. Its papers remain available to read, and contributors can propose a formal statement of a result. Suggest a change
The release contains no Lean statement for this family, so there is no formal statement to compare with OpenAI’s description.
Other people’s accounts of running proof-verification software, with links to their reports.
Yao Xu, feat(ErdosProblems/181): mark solved and link the formal proof (PR 7128, fixes issue 6906), 11 October 2026. Source
Reported: leanchecker --fresh replay exit 0 after 1334 s, Comparator accepted with Lean’s kernel, plus a second nanoda run, on a 32-core cloud VM.
These links come from the papers’ bibliographies. A citation records that one paper cites another; how each cited result is used has not been examined here.
This family’s papers cite no paper elsewhere in the release.
No paper elsewhere in the release cites this family’s papers.
Yao Xu, feat(ErdosProblems/181): mark solved and link the formal proof (PR 7128, fixes issue 6906), 11 October 2026. Source
Erdős 181 marked solved with a formal_proof link pinned to the v1.0.0 release commit.
The Justin Sun Prize, The Justin Sun Prize: problem bank and award records, 11 October 2026. Source
JSP-000175 lists the release’s claim as Solved with independent mathematical review pending; Lean proof column: No.
Yao Xu, The hypercube Ramsey number has linear order, in Lean 4 (Erdős 181), 8 October 2026. Source
Lean proof of Erdős 181 following the release’s manuscript, built on the release’s cube Ramsey library.
Each paper’s outside references are listed with it on its reading page, where each citation is placed. Every outside work cited in the release: References outside the release
Atlas has no contributed explanation for this family yet. You can offer one with a GitHub account. You receive named credit and disclose any AI assistance.
Each button opens a GitHub form with this page and its source version filled in. Opening the form does not reserve the work.
Offer to write an explanationSuggest a source attributionSuggest a change
Commentary on this family by others, dated and credited. It is commentary, not a finding.
An unsigned public tier list, the OpenAI Math Tier List, classes it as a proof and rates its significance, if it holds up, as “Major math journal”. The page says that nothing on it is verified.
Author not stated. Source
Thomas Bloom, Erdős problems in the OpenAI proofs, 8 October 2026. Source
Bloom lists Erdős 181 (hypercube Ramsey number of linear order), names Tikhomirov’s earlier bound, and says it is not formalised and the PDF has 172 pages.
mo271, ErdosProblems/181: erdos_181 is true (issue 6906), 7 October 2026. Source
The hypercube Ramsey manuscript proves R(Q_n) <= C 2^n, exactly the formal statement.
Each item identifies a statement, definition or report that needs further review. Its link opens a GitHub form with the source version already recorded.
Why this passage is shown
Theorem 1.1
In The hypercube Ramsey number has linear order, 23 September 2026