The Schwartz Quadratic Meander Number Conjecture
A cyclic meander induces a cyclic permutation on its marked intersection points. Schwartz's conjecture on the quadratic growth of the associated meander number is resolved.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Combinatorics
- Posed by
- Richard Evan Schwartz
- Year posed
- —
- Years open
- —
- Solved
- 2026-06-10
- Model
- ChatGPT 5.5, Claude Opus 4.7, Gemini 3.1
- Vendor
- OpenAI / Anthropic / Google
- Collaborators
- Charles Daly, Diaaeldin Taha
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The authors say the models were used as research assistants, mainly to explore potentially relevant directions, alongside their own computational experiments. No specific step is attributed, so the lowest tier applies.
Verification
arXiv preprint; not yet peer-reviewed.
Source
arXiv:2606.12331 - Resolving the Schwartz Quadratic Meander Number Conjecture