Source authenticated

Borsuk Conjecture lowest-ever counterexample (N=63)

Priority: the result was first obtained by Max Grinsztajn with GPT-5.5 Pro assistance, published 26 May 2026 and recorded as the current best bound on Tao's optimization-problems ledger. The same construction was found again independently in August 2026 by Nicholas Konz working with Claude, with a different derivation and a fuller AI disclosure; the two efforts were evidently unaware of each other, and the submitter of this entry surfaced the earlier work themselves after publication. Dimension 63 is the current record; whether Borsuk's conjecture fails for any dimension in 4..62 remains open.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: May 26, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: site-confirmed. Publication: preprint. AI contribution: ai-assisted. Imported under CC BY 4.0.

Canonical aliases: Borsuk Conjecture lowest-ever counterexample (N=63) · Borsuk Counterexample N=63

Confidence: Not scored

Registry verification: site confirmed · preprint · partial

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

Max Grinsztajn
human · human collaborator

GPT-5.5 Pro
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Borsuk Conjecture lowest-ever counterexample (N=63)

specialist registry · passed

Both derivations reproduced by this site on 12 August 2026, independently of each other. For the first solve (Grinsztajn, May 2026): the repository's exact verifier - pure Python integer arithmetic over F16, read before running - was executed locally and passes all checks: it rebuilds the G2(4) strongly regular graph with parameters (416,100,36,20), the B1/B2/B3/C partition and degree data behind the dimension drop, and the clique obstructions forcing every smaller-diameter subset to size at most 5. The repo's GitHub creation date of 2026-05-26 is not forgeable after the fact, and Terence Tao's optimization-problems ledger (constant 28a) independently credits the 63 bound to Grinsztajn, citing this repository. For the August rediscovery (Konz + Claude): we ran the author's stand-alone verifier against the published 321x63 coordinate file and confirmed affine dimension exactly 63, the squared-distance spectrum (53-sqrt(222))/156, 1/4 and 1/3, and independence number 5 for the diameter graph by Bron-Kerbosch, forcing ceil(321/5) = 65 parts where Borsuk allows 64; the distance-class gap is far wider than any float tolerance. Neither write-up is peer-reviewed; neither is on arXiv.

Source ↗

Independent rediscovery by Konz + Claude, August 2026: write-up, coordinates and verifier

independent reproduction · passed

independent link supplied by the VibeMathed registry.

Source ↗

Borsuk Conjecture lowest-ever counterexample (N=63)

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Tao's optimization-problems ledger, constant 28a - credits the 63 bound to Grinsztajn

specialist registry · pending

problem-record link supplied by the VibeMathed registry.