GPT-5.6 Proves Graph Theory Conjecture

量子位 · wechat · 2026-07-11

The article details how an OpenAI researcher used GPT-5.6 Sol Ultra to draft a proof for the Cycle Double Cover Conjecture in under an hour, a classic open problem in graph theory.

The summary breaks down the proof approach: reducing general graphs to cubic graphs, applying the nowhere-zero 8-flow theorem to assign 3-bit binary labels to edges, expanding these into two labels so edges with the same label automatically form cycles, and finally achieving global consistency via systems of linear equations, dual spaces, and parity arguments.

Another key focus is OpenAI's published prompt design methodology:

Instead of forcing rigid steps, it clearly defines what constitutes "completion".
It establishes boundary conditions for graphs, bridges, cycles, and covers.
It explicitly lists results that "do not count as an answer".
It leverages up to 64 sub-agents for dynamic search, incorporating independent reviews and adversarial checks.

The author concludes that the true takeaway isn't the prompt's length, but how it transforms a complex task into a verifiable, auditable, and correctable contract.

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GPT-5.6 Proves Graph Theory Conjecture

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