What was already known
Canonical ampleness was known under stronger negative or quasi-negative holomorphic sectional curvature assumptions, and under Kähler hyperbolicity. Those metric hypotheses are distinct from the absence of entire curves (manuscript introduction, pp. 1–2).
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 Kobayashi’s canonical-ampleness conjecture in the smooth compact Kähler category.
Limitations
The statement is for compact connected Kähler manifolds; it does not cover singular or noncompact spaces.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.
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, and prior-work review for non-notifying local inclusion.
Read this published revision