Cycle Double Cover Conjecture
Conjectures that every bridgeless graph has a collection of cycles covering each edge exactly twice.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Graph Theory
- Posed by
- George Szekeres, Paul Seymour
- Year posed
- 1973
- Years open
- 53y
- Solved
- 2026-07-10
- Model
- GPT-5.6 Sol Ultra
- Vendor
- OpenAI
- Collaborators
- —
- Verification
- Lean-checked, statement unaudited
- Publication
- Announced
- Significance
- 55 / 100
- Disclosed cost
- —
- Wikipedia
- 2 languages
What the AI did
Running in Ultra mode with 64 parallel subagents, GPT-5.6 Sol produced a claimed proof of the full Cycle Double Cover Conjecture in under an hour. OpenAI released both the proof manuscript and the task prompt; a public Lean formalization was added afterwards.
Verification
Announced by OpenAI researcher Ethan Knight on 10 July 2026, timed to the GPT-5.6 Sol Ultra release. Not peer-reviewed; the Cycle Double Cover Conjecture has a history of claimed proofs later found to have gaps, so mathematicians are treating it cautiously pending independent review. Lean released here: https://github.com/openai/cdc-lean