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Research / Sep 3, 2026

Köthe conjecture via Krempa's matrix formulation

Must matrices over a nil two-sided ideal form a nil ideal, as in Krempa's formulation equivalent to Köthe's conjecture?

Model / AI: GPT-6 Astra

machine-checked (matrix-form counterexample)self-reported (matrix-form counterexample)
Sep 3, 2026

Autonomous Lean counterexample

Model / AI: GPT-6 Astra

machine-checked (matrix-form counterexample)self-reported (matrix-form counterexample)

A pre-release GPT-6 Astra run in Epoch AI's LeanOpenProblems harness constructed a nil ideal over the algebraic closure of F2 whose 2 by 2 matrix ideal contains a non-nilpotent element. The repository reports one network-isolated attempt with no human steering, then packages the result for Comparator against the benchmark statement.

Source read 2026-09-08. Read the repository's theorem, fidelity, provenance and verification sections. The Lean build and the 1972 equivalence were not independently checked here.