What was already known
K-convexity was known to imply finite cotype on both sides. Recovering K-convexity from that pair of cotype conditions was the unresolved direction; the manuscript establishes it under the ordinary approximation property.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Resolves the cotype–cotype conjecture for the broad class of Banach spaces with the approximation property.
Limitations
The converse direction depends on the approximation property; the paper does not claim the equivalence for all Banach spaces.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note proves the equivalence for every nonzero real Banach space with the ordinary approximation property.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For a nonzero real Banach space with the ordinary approximation property, K-convexity holds if and only if both the space and its dual have finite Rademacher cotype, with possibly different exponents.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision