Neuro-symbolic system proves van der Waerden number w(2;3,21)=416 with Lean 4 check
Rodriguez909 · reddit · 2026-10-30
The van der Waerden number w(2;3,21) = 416 has been proved with a Lean 4 kernel-checked proof, resolving a conjecture Kullmann made in 2010 that DeepMind's Formal Conjectures list still carried as open this year.
- Statement: every red-blue colouring of {1,...,416} contains a red 3-term or blue 21-term arithmetic progression; some colouring of {1,...,415} contains neither
- Scale: 209 cases and 38,661,140 leaf formulas, each refutation checked by cakepr (the LRAT checker verified in CakeML) and digest-bound to its Lean term
- Generated by LPM (Large Proof Model), a neuro-symbolic system from Hupyy; nothing counted unless the Lean kernel or cakepr accepted it
- A 13.6GB evidence package (Lean sources, checker records, replay kit) is publicly available
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