OpenAI Claims a GPT-5.6 Configuration Produced a Proof of a 50-Year-Old Graph Conjecture

OpenAI published a paper attributing a proof of the Cycle Double Cover Conjecture, a graph-theory problem open since the 1970s, to a system it identifies as GPT-5.6 Sol Ultra, according to reporting aggregated from the release. The conjecture, posed independently by George Szekeres in 1973 and Paul Seymour in 1979, holds that any bridgeless graph admits a collection of cycles covering every edge exactly twice. The AI Post channel reports that the model deployed 64 agents in parallel and returned the argument in under an hour.

Early expert reaction is mixed in a telling way. Thomas Bloom, a mathematician, called the proof "very nice" and "elementary," saying it could have been found in the 1980s, while criticizing its lack of citations to foundational prior work. On Hacker News, readers are still working through the PDF. Importantly, the proof has not been peer-reviewed or formally verified.

The honest read splits into two outcomes. If the proof survives formal checking, it is a concrete instance of a model closing a decades-old open problem through parallel search and verification, not merely competition-style problem solving. If reviewers find a gap, it becomes a cautionary example of a lab announcing a result before validation. What decides between these outcomes is independent verification, ideally machine-checked in a proof assistant.