OpenAI reports Gepner stability on every smooth quintic threefold

Every smooth complex quintic threefold admits a numerical Bridgeland stability condition with the support property whose hyperplane-tensor and structure-sheaf spherical-twist symmetry shifts phase by 2/5, with the normalized central charge of Toda’s quintic Gepner conjecture.

Sources for this record

What was already known

Li established numerical Bridgeland stability conditions on every smooth quintic. Toda had specified the Gepner central charge and tilt construction but left Harder–Narasimhan filtrations at the irrational charge unresolved; the manuscript adds the prescribed symmetry (manuscript introduction, Prior work and the remaining construction, pp. 1–2).

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 Toda’s normalized quintic Gepner conjecture for every smooth complex quintic threefold.

Limitations

The claim concerns smooth quintic threefolds and a numerical stability condition with the specified normalization; it is not a construction for arbitrary Calabi–Yau threefolds.

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.

Read this published revision