The cycle double cover conjecture, posed in the 1970s by W. T. Tutte and independently by others including Paul Seymour, asks whether every bridgeless graph has a cycle double cover, a collection of cycles that together cover each edge of the graph exactly twice. A July 2026 preprint from OpenAI claimed a positive resolution, attributed to their GPT-5.6 model, a claim not yet independently confirmed.
Facts
Partially Attested
Progress Toward ResolutionIn July 2026 OpenAI announced a claimed proof found by its GPT-5.6 Sol Ultra model, with a released three-page proof and Lean formalization. 1 The July 2026 claimed proof by OpenAI was announced with a Lean formalization but independent confirmation is not established here. Prize Status
Prize Status (category) StatementWhether every bridgeless graph has a cycle double cover, a collection of cycles covering each edge exactly twice. 1 Classification
Resolution Status Chronology
Resolved Year Connections
Posed By
Source Cycle Double Cover (Wikipedia)
Sources
1. Cycle Double Cover (Wikipedia)
Lead section
whether every bridgeless graph has a cycle double cover
Recent developments
OpenAI announced on Twitter that their GPT-5.6 Sol Ultra large language model had found a proof of the conjecture
Posed By: W. T. Tutte, Lead paragraph
It is a problem posed in the 1970s by W. T. Tutte, Itai and Rodeh, George Szekeres and Paul Seymour and known as the cycle double cover conjecture, whether every bridgeless
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