What was already known
Beauville formulated compatible universal-cover splitting and proved major cases, including Kähler–Einstein manifolds and compact Kähler surfaces; the general two-summand integrable case remained the manuscript’s target.
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 two-summand integrable form of Beauville’s compatible splitting question.
Limitations
Both summands must be integrable. Automatic integrability and other corollaries are separate from the selected claim.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note gives the product of simply connected complex manifolds with differential identifying the factors with both specified integrable summands.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- If the tangent bundle of a compact connected Kähler manifold splits into two positive-rank integrable holomorphic subbundles, its ordinary universal cover is a product whose tangent factors lift the specified summands.
- 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