GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

What happened

On July 10, 2026, OpenAI announced that GPT-5.6 Sol Ultra produced a proof of the Cycle Double Cover Conjecture (CDC) — a 50-year-old open problem in graph theory — using 64 parallel subagents in under one hour.

Context and impact

CDC was formulated independently by George Szekeres (1973) and Paul Seymour (1979) and is considered one of the most significant open problems in combinatorics. If the proof survives independent review, it would mark a historic milestone for AI in pure mathematics — comparable to AlphaProof at IMO 2024. The mathematical community is actively verifying the result.

Details

• Model: GPT-5.6 Sol Ultra (Ultra = multi-agent mode with subagent orchestration)
• Technique: 64 parallel subagents, under 60 minutes to solution
• Approach: proof focuses on the class of loopless cubic graphs
• OpenAI published the full PDF proof (cdn.openai.com) and the prompt
• Announced via X by Ethan Knight (OpenAI), the day after Sol Ultra's global release (July 9)
• Proof is currently in peer review — not yet independently verified