What was already known
The Shafarevich conjecture predicted holomorphic convexity of universal covers of projective varieties, and Steinness in the large-fundamental-group case. Positive results covered projective varieties with suitable linear fundamental-group representations; unrestricted groups remained (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
Disproves Shafarevich’s holomorphic-convexity conjecture even under its large-fundamental-group hypothesis.
Limitations
The construction is a complex projective fourfold; it does not give a counterexample in lower dimensions or to linear Shafarevich results.
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