Jenrich and Brouwer (2014), A 64-dimensional counterexample

../

theorem_1: A two-distance set of 352 points in R^64 requires at least 71 parts in every partition into subsets of smaller diameter.

---

Thomas Jenrich and Andries E. Brouwer, A 64-dimensional counterexample to Borsuk's conjecture, Electronic Journal of Combinatorics 21(4) (2014), P4.29, 3 pages. DOI: 10.37236/4069. The official published PDF records submission on 3 February 2014, acceptance on 28 October 2014, and publication on 6 November 2014, all on p. 1. No notice is printed beyond the page footer "the electronic journal of combinatorics 21(4) (2014), #P4.29"; the journal's article page shows no copyright or license (https://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i4p29, read 2026-10-02), and the journal's submissions page states that "The copyright of published papers remains with the current copyright owner (usually the authors)" and that "Most papers published before March 31, 2018 did not contain explicit copyright or license statements.", so the authors' copyright governs with no reuse grant stated, every other right reserved.

The journal record and official PDF were checked.

Digest

theorem_1 provides a counterexample to E0505 in dimension 64. The proof uses the Euclidean representation of the $G_2(4)$ graph underlying Bondarenko's construction and a partition arising from the Suzuki graph structure. It places 352 points in a hyperplane of a 65-dimensional representation and retains the bound of five points per smaller-diameter subset.

This three-page joint publication is distinct from jenrich_2014_two_distance_borsuk_counterexample, the seven-page solo arXiv manuscript. The publication's reference [5] points to solo arXiv v5 for an explicit construction and program; the solo copy retained in this corpus is v6. The two sources keep separate identities, PDFs, and locators.

Reading and proof scope

All three published pages were visually checked for source identity, the statement, and its proof dependencies, including Theorem 1 on p. 3. The result page states the theorem and identifies its proof and dependencies. It does not yet provide a complete rewritten proof or an independent review of all graph-theoretic inputs. The checked published dimension-64 result and the borsuk_dimension_63_public_claims are recorded separately.

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