AI agents settle all 15,973 semigroups of order 6 with 5M lines of verified Lean
KyleCranmer · x · 2026-10-03
- A team used multiple AI agents (Codex and Claude Code) working intensively for 3 months to classify all 15,973 semigroups of order 6: explicit finite bases were written down for the first time for the 15,969 that have one, and the remaining 4 were proved to have none.
- Most of these bases had never been explicitly written down before. The Lean formalization, orchestrated via a multi-agent approach, produced over 5 million lines of verified Lean code — one of the largest auto-formalization projects to date.
- Collaborators include JanotaMikolas, JanHula, and semigroup experts João Araújo and Edmond W. H. Lee.
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