OpenAI reports Donovan’s conjecture over algebraically closed fields

For every algebraically closed field K of characteristic p>0 and every fixed bound on defect-group order, blocks of finite groups represent only finitely many K-linear Morita-equivalence classes.

Sources for this record

What was already known

Donovan’s conjecture was known for selected block families and was reduced to Cartan boundedness and rationality-type constraints. The manuscript removes the abelian-defect restriction and includes characteristic two.

AI involvement AI-led

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 Major

Resolves Donovan’s finiteness conjecture over algebraically closed fields without restricting defect groups to be abelian.

Limitations

The field K and defect-order bound are fixed before the finite groups vary; the claim is K-linear Morita finiteness, not a bound uniform across all fields. No completed proof check was documented in the available sources.

Technical verification Reported

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

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

2026-10-18 · publication

Primary manuscript, attribution, and prior-work review for non-notifying local inclusion; technical check remains undocumented.

Read this published revision