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Research / Oct 6, 2026

A torsion-free hyperbolic group that is not residually finite

Can the mathematical statement in A torsion-free hyperbolic group that is not residually finite be proved and verified machine-checked in Lean?

Model / AI: OpenAI (unreleased)

machine-checked (formal proof)self-reported (formal proof)
Oct 6, 2026

Lean formalization in OpenAI math repository (Result 252)

Model / AI: OpenAI (unreleased)

machine-checked (formal proof)self-reported (formal proof)

OpenAI's internal frontier model proved and formalized in Lean the main result of 'A torsion-free hyperbolic group that is not residually finite'. We construct a torsion-free word-hyperbolic group that is not residually finite, answering the residual-finiteness question for hyperbolic groups negatively.

Source read 2026-10-08. Cataloged from OpenAI's formalization.yaml (Family 252). The Lean development was not rebuilt locally.