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Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

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Yibo Ji, An AI Generated Counterexample to Borsuk Problem in Dimension 63, arXiv:2608.12561v1, submitted 12 August 2026, 15 pages; the PDF's own title line reads "An AI-Generated Counterexample to Borsuk's Problem in Dimension 63". Theorem 6.2 claims a set XX of 321 points in R63\mathbb R^{63} of diameter 8\sqrt8, with squared distances 6 or 8 between the original points and 8−2t8-2t or 8 from the added point, whose smaller-diameter subsets have at most five points, so that at least 65 parts are needed where the question allows n+1=64n+1=64; rescaling by 1/81/\sqrt8 gives the unit-diameter form. The abstract says that ChatGPT using GPT-5.6 Sol generated the example and the proof; Ji reports checking the result personally, takes responsibility for that check and claims no originality, and a first-page footnote says Ji's name appears as author only for submission purposes. Appendix A prints a verification script. The corpus records the statement at Theorem 6.2 of the source card.

Withdrawal. Version 2 of 14 August 2026 withdraws the submission. Its comment says the submitter had found the counterexample already posted at Grinsztajn's repository and on Nicholas Konz's page; it identifies no mathematical error, and the record offers no v2 text. The claim therefore stands as withdrawn, not refuted. The same construction, with its priority, is recorded on Grinsztajn's claim page. No run of the script or review of the proof is recorded.