GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
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GPT-5.6 Sol Ultra produces a claimed proof of the Cycle Double Cover Conjecture.
The paper claims to prove the Cycle Double Cover Conjecture, which states every bridgeless undirected graph has a collection of cycles covering each edge twice. The proof reduces to cubic graphs, uses a nowhere-zero 8-flow, and converts it into a labeling of edges by two-element sets of F2^3. The argument culminates in a linear algebra duality lemma. The authors state the proof is entirely due to GPT-5.6 Sol Ultra and the writeup with Codex.
What commenters are saying
Commenters are skeptical of the proof's correctness, noting it is very short and uses no mathematics developed in the last 30 years. Some question whether the proof has been verified by humans or in Lean, and point to a GitHub repository for a Lean formalization. Others discuss the prompt strategy, including asking the model to spend at least 8 hours and to assume a complete affirmative proof exists. There is discussion of the cost and the survivorship bias of such attempts.