What was already known
Wu and Yau formulated a two-sided negatively pinched Kähler uniformization question. Earlier intrinsic-metric comparisons did not produce bounded holomorphic coordinate functions; a different companion example had only one-sided curvature control.
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
Answers the two-sided negatively pinched Kähler uniformization question negatively.
Limitations
The example has two bounded nonconstant holomorphic functions; the obstruction is to a full bounded coordinate system with independent differentials.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note constructs the complete two-sided negatively pinched Kähler threefold and proves absence of bounded holomorphic coordinates and bounded-domain realization.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- There is a contractible complex three-dimensional domain with a complete Kähler metric whose real sectional curvatures lie between two negative constants, yet it has no bounded holomorphic map to complex three-space with nowhere-vanishing Jacobian and is not biholomorphic to a bounded domain.
- 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