Norine's Antipodal-Colouring Conjecture
Norine conjectured that every red-blue edge-colouring of the -dimensional hypercube in which antipodal edges get opposite colours contains a monochromatic path from some vertex to its antipode. The paper proves it, via a chain-level Borsuk–Ulam obstruction.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Graph Theory, Topological Combinatorics
- Posed by
- Serguei Norine
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-21
- Model
- GPT-5
- Vendor
- OpenAI
- Collaborators
- Hehui Wu, Ningyuan Yang
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The authors state the central proof idea was first generated with the assistance of GPT-5, and that the manuscript was drafted with Codex.
Verification
No independent check. The model is credited with the central idea rather than the whole argument. Preprint, not refereed.
Source
- PaperarXiv