Published November 9, 2026
| Version v1.0.1
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R(12,12) ≥ 1661: a colouring of K_1660, a Lean proof and computer checks
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Description
A red/blue colouring of the complete graph on 1660 vertices with no monochromatic K_12, so R(12,12) ≥ 1661. It consists of the Mathon–Shearer colouring M(797) with 21 vertices removed, and 85 core vertices, each a copy of a removed vertex or constant on the rest of M(797). The removed vertices contain two antipodal pairs of M(797). Checked by two independent exhaustive computer searches and by a clone-projection argument with an antipodal rule, and proved in Lean 4 with Mathlib; the compiled proof was also accepted by leanchecker and by the independent kernel nanoda. The work was done with Claude (Claude Opus 5.5, Anthropic); see the README.
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YueMa0/r1212-1661-v1.0.1.zip
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- Is supplement to
- Software: https://github.com/YueMa0/r1212-1661/tree/v1.0.1 (URL)
Software
- Repository URL
- https://github.com/YueMa0/r1212-1661