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.
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
Sections 6–7 document Lean checking of reductions and 55 classification certificate pairs, one-to-one CNF/input-hash comparisons and two solvers’ UNSAT outcomes for all 56,723 formulas. The final UniformK61.WholeProof.ramsey61 theorem still takes the SAT exclusions as a premise, so the complete upper bound is rated Partial.
- Supporting source (arxiv.org) — Completed checking report and its limits
Human understanding
Tatarevic’s proof roadmap explains the neighbourhood deficits, ticket double count, exceptional C branch and perfect-balance obstruction, with the finite computational obligations separated in Section 6.
Correction and publication history
Lists the original paper once while retaining the specific checking and provenance references. Research claims and rating levels are unchanged.
Read this published revisionClarifies that the source reports completed checking but does not supply its exact completion date. Research claims and rating levels are unchanged.
Read this published revisionNewly reviewed source-backed research contribution with contribution-specific AI attribution and checking limits.
Read this published revision