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Research / Oct 6, 2026

A proof of Seymour’s second-neighborhood conjecture

Can the mathematical statement in A proof of Seymour’s second-neighborhood conjecture 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 173)

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 proof of Seymour’s second-neighborhood conjecture'. We prove that every nonempty finite oriented graph has a vertex with at least as many vertices at directed distance two as at directed distance one. This resolves Seymour's second neighborhood conjecture positively.

Source read 2026-10-08. Cataloged from OpenAI's formalization.yaml (Family 173). The Lean development was not rebuilt locally.