What was already known
Fettes, Kramer and Radziszowski proved the upper bound 62 in 2004. The 2026 Small Ramsey Numbers survey gives 51≤R(3,3,3,3)≤62. The new claim improves the upper endpoint by one, without determining the exact number.
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AI involvement
Section 7 assigns the A/B/D reductions to GPT-5.6 and Fable, and the C reduction, integration and simplified compatibility argument to GPT-6 Astra. Tatarevic directed the research and computations. These specified mathematical reductions support AI-centered inclusion, beyond code generation alone.
Importance
A concrete improvement to a longstanding finite Ramsey bound, with a detailed reduction and reproducible computational record.
Limitations
Lean checks the reductions, finite classifications and input-generation correspondence, but its final theorem assumes that all 56,723 formulas are unsatisfiable. Two SAT solvers reported UNSAT on every generated input; these exclusions are not checked by Lean in this artifact. The exact Ramsey number and a stronger lower bound remain unresolved.
Technical verification
Correction and publication history
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