What was already known
Griffiths’ conjecture asked whether ampleness of a holomorphic vector bundle on a smooth complex projective variety implies a strictly Griffiths-positive Hermitian metric; the converse implication was known.
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
Disproves the modern formulation of Griffiths’ positivity conjecture already in rank two on a quadric surface.
Limitations
The selected result covers the rank-two family and sufficiently large powers for failure of positivity. Its separate very-ampleness assertion is outside the Lean scope.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note identifies ampleness for every positive power and lack of a strictly Griffiths-positive metric for all sufficiently large powers.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- On P¹ × P¹, coordinatewise power pullbacks of an explicit rank-two bundle, tensored with O(1,1), are ample for every positive power yet admit no smooth strictly Griffiths-positive Hermitian metric for all sufficiently large powers.
- 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