Ji (2026), historical v1 of a withdrawn Borsuk submission

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lemma_4_1: The elementary lemma behind the added point of Ji's withdrawn v1: if an outside vector meets equal-norm points of a subspace at two inner-product levels, a scalar multiple of its projection sits at the target distance from one level and strictly closer to the other.

proposition_6_1: The graph identification behind Theorem 6.2 of Ji's withdrawn v1: two points of the 321-point set lie strictly closer than its diameter exactly when their labels are adjacent in the G_2(4) graph.

theorem_6_2: Ji's retained arXiv v1 claims 321 points of diameter sqrt(8) in R^63, with at most five points in any subset of strictly smaller diameter.

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Yibo Ji, An AI Generated Counterexample to Borsuk Problem in Dimension 63, arXiv:2608.12561v1, submitted 12 August 2026 at 20:03:44 UTC, 15 pages, math.MG; the PDF's own title line reads "An AI-Generated Counterexample to Borsuk's Problem in Dimension 63". The copy read for this card is the v1 PDF. The arXiv record names arXiv's non-exclusive distribution license (arXiv:2608.12561), every other right reserved.

The current arXiv record is the withdrawn v2, dated 14 August 2026 at 00:39:52 UTC. Its comment says the submitter had found that the counterexample was already posted at Grinsztajn's repository and Nicholas Konz's page. The stated reason concerns prior posting; it does not identify a mathematical error. The record offers no v2 PDF. The retained v1 is historical content of this withdrawn submission, not a current unwithdrawn preprint.

Claim and provenance

The theorem_6_2 claim concerns 321 points in dimension 63 and a lower bound of 65 on the number of smaller-diameter parts. The abstract says ChatGPT using GPT-5.6 Sol generated the example and proof. Ji reports personally verifying the result, taking responsibility for that verification, and claiming no originality credit. The first-page footnote says Ji's name appears as author solely for formal submission purposes.

The earlier grinsztajn_2026_borsuk_dimension_63_claim remains a separate source. The chronology and the Konz rediscovery report are recorded at borsuk_dimension_63_public_claims.

Results recorded

• Theorem 6.2 (p. 7), the main claim: a 321-point set in $\mathbb R^{63}$ of diameter $\sqrt8$ whose subsets of smaller diameter have at most five points, so $b(63)\ge65$.
• Proposition 6.1 (p. 7), the identification of the set's compatibility graph with the $G_2(4)$ graph induced on the 320-point core and one outside vertex.
• Lemma 4.1 (p. 5), the projection-shadow lemma that places the added point.

Section 2 (pp. 2--4) sets up the $G_2(4)$ realization in $\mathbb R^{65}$ and the equitable partition, Section 3 (pp. 4--5) places the 320-point core in a 63-dimensional subspace, and Section 5 (pp. 5--6) builds the added point. Appendix B (p. 14) states the construction as a general "reusable blocker template" in five conditions, without a theorem.

Reading and proof scope

The statements of Sections 2--6 (pp. 2--7) were read clause by clause on the PDF; pp. 1, 7 and 8 were also checked for the diameter normalization, the AI disclosure and the verification description. Section 8 and Appendix A describe and print verification code. No code or certificate was executed or audited, and the full proof was not independently reviewed. Personal verification is a source attestation. Neither it nor the withdrawal notice supplies independent proof verification or peer-reviewed acceptance.

Bears on

• E0505: Theorem 6.2, rescaled to diameter one, claims a set in $\mathbb R^{63}$ that is not the union of 64 sets of smaller diameter, a negative answer to the question in dimension 63; unreviewed here, and the submission is withdrawn. Proposition 6.1 and Lemma 4.1 bear on the problem only through it.

No file of this source is held: no license on record permits its redistribution, and the card cites the edition it names above.