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Research / Oct 6, 2026

The cotype–cotype conjecture under the approximation property

Can the mathematical statement in The cotype–cotype conjecture under the approximation property 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 326)

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 'The cotype–cotype conjecture under the approximation property'. We prove the cotype–cotype conjecture under the ordinary approximation property. A nonzero real Banach space with this property is K-convex if and only if both the space and its dual have finite Rademacher cotype, possibly with different exponents.

Source read 2026-10-08. Cataloged from OpenAI's formalization.yaml (Family 326). The Lean development was not rebuilt locally.