Feige's Hypergraph Moore-Bound Conjecture
At the conjectured density, must every -uniform hypergraph contain a short nontrivial even cover - a set of hyperedges covering each vertex an even number of times - with no superfluous polylogarithmic factors? Known up to polylog factors since 2022; now proved exactly for every .
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Extremal combinatorics
- Posed by
- Uriel Feige
- Year posed
- 2008
- Years open
- 18y
- Solved
- 2026-07-17
- Model
- GPT-5.6 Sol, GPT-5.5 Pro, Claude Opus 4.8, Claude Fable 5
- Vendor
- OpenAI / Anthropic
- Collaborators
- —
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 25 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The colored-walk polynomial-interpolation argument over Kikuchi graphs was developed across several frontier models and written up by a five-author team, with an independent spectral proof alongside.
Verification
Five-author arXiv preprint plus an independent spectral proof of the same bound. Not yet peer-reviewed.