Published November 1, 2026 | Version v1.1.0

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.

Notes

If you use this colouring, please cite it as below, together with Tatarevic's paper and r1212-1642.

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YueMa0/r1212-1658-v1.1.0.zip

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