OpenAI Claims GPT-5.6 Sol Ultra Proved the Cycle Double Cover Conjecture

OpenAI has posted a document on its CDN claiming that the GPT-5.6 Sol Ultra language model has produced a proof of the Cycle Double Cover Conjecture — one of the well-known unsolved problems in graph theory.

The material was published as a PDF via a direct link on OpenAI's servers, without an accompanying press release or a separate article offering any explanation.

The Community's Reaction

The publication quickly climbed to the top of Hacker News, where, at the time of writing, it had gathered 179 points and drawn 165 comments. The level of activity suggests that the claim caught the attention of both artificial intelligence specialists and mathematicians, though the details of the discussion are not reported in the available sources.

What Is Known and What Is Not

The available description says nothing about whether the proof has undergone independent review by the mathematical community, which of OpenAI's researchers worked on the problem, or what methods were used to generate the proof. Nor is it stated how the model formulated and set out its mathematical reasoning, or whether any auxiliary tooling for formal verification was used.

The Cycle Double Cover Conjecture is a classic problem in graph theory and a subject of interest for specialists in discrete mathematics. The appearance of a claimed solution from a language model, if confirmed, could become a notable moment in the debate over the applicability of large language models to formal mathematical proofs.

As it stands, the available materials do not allow us to assess the correctness or completeness of the presented proof — the editorial team will be following how the situation develops and how the scientific community responds.

Source: Hacker News