Published November 1, 2026
| Version v1.1.0
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R(12,12) ≥ 1658: a colouring of K_1657, a Lean proof and computer checks
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Description
A red/blue colouring of the complete graph on 1657 vertices with no monochromatic K_12, so R(12,12) ≥ 1658. It consists of the Mathon colouring M(797) and 61 added vertices, each a copy of a certificate vertex or constant on the rest of M(797). Checked by an exhaustive computer search and by a clone-projection argument, 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), starting from exploratory work by GPT-6 Astra (OpenAI); see the README.
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YueMa0/r1212-1658-v1.1.0.zip
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- Is supplement to
- Software: https://github.com/YueMa0/r1212-1658/tree/v1.1.0 (URL)
Software
- Repository URL
- https://github.com/YueMa0/r1212-1658