What was already known
Earlier Eisenbud–Green–Harris Hilbert-function results and lex-plus-powers Betti bounds required split forms or degree-growth assumptions; the manuscript removes those restrictions in characteristic zero.
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 Eisenbud–Green–Harris and lex-plus-powers conjectures in the stated characteristic-zero setting.
Limitations
The selected claim is characteristic zero and requires a homogeneous regular sequence with all degrees at least two. No completed proof check was documented in the available sources.
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; technical check remains undocumented.
Read this published revision