Definition
The Cycle Double Cover Conjecture is a graph theory problem (posed ~1973–1979 by Tutte, Szekeres, Seymour, and others) asserting every finite bridgeless undirected graph has a collection of cycles covering each edge exactly twice.
OpenAI Claim (July 2026)
- 2026-07-10: openai claims gpt-56 Sol Ultra produced candidate proof in <1 hour using 64 parallel subagents (2026-07-12-openai-gpt-56-sol-ultra-cycle-double-cover-proof)
- Published 3-page PDF and full prompt; proof reduces to cubic graphs via 8-flow theorem
- Mathematician Thomas Bloom called proof “very nice” and “elementary” but criticized missing 1983 Bermond-Jackson-Jaeger citations
Candidate proof only — not peer-reviewed, no Lean/Coq machine verification. Conjecture has history of flawed proofs.
Related
- formal-verification
- automated-theorem-proving
- openai
- gpt-56
- multi-agent-systems
- test-time-scaling
- ai-for-science