What was already known
The corresponding previous bounds were 60, 99, 138, 147, 158, 170, 205, 213 and 234.
AI involvement
Nagda, Raghavan and Thakurta designed the objective and evaluator. AlphaEvolve evolved the retained search algorithms and produced the witness graphs.
The retained AI-generated search algorithms found the nine witness graphs inside a human-designed evaluator and campaign.
Importance
Raises nine finite Ramsey lower bounds through new graph witnesses.
Limitations
These are graph-existence lower bounds, not exact Ramsey numbers. The released matrices and verifier are available, but the notebook has no saved run output and a completed independent exact check of all nine witnesses is undocumented.
Technical verification
The evaluator-guided search tests clique and independent-set constraints, and matrices plus an exact verification notebook are released. The notebook has no saved execution output and no completed independent check of all nine matrices is documented, so the available evidence supports partial source-reported testing, not a completed exact certificate audit.
Human understanding
The human authors explain the graph-witness logic, evaluator, initialization families and comparison with earlier heuristics.
Correction and publication history
Raises nine finite Ramsey lower bounds through new graph witnesses.
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