A Ramsey-style open problem on hypergraphs from Epoch AI's FrontierMath benchmark has been solved by GPT-5.4 Pro, as elicited by Kevin Barreto and Liam Price. The problem involved constructing hypergraphs as large as possible without a specific partition property, improving known lower bounds by a constant factor. Problem contributor Will Brian confirmed the solution, noting it eliminates an inefficiency in the prior lower-bound construction and mirrors the upper-bound construction. The solution is being written up for publication. Subsequently, other frontier models including Opus 4.6, Gemini 3.1 Pro, and GPT-5.4 also solved the problem using a general scaffold for testing. The problem was estimated to take a human expert 1–3 months to solve.
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