OpenAI reports the ordinary-double-point volume gap

A singular n-dimensional complex algebraic klt germ with zero boundary has normalized volume at most 2(n−1)^n, with equality exactly at an analytic ordinary double point.

Sources for this record

What was already known

The manuscript presents the sharp equality and gap statement as a conjecture not previously known in all dimensions.

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 Notable

Gives a sharp dimension-uniform bound and characterizes its equality case.

Limitations

The claim is for boundary-zero complex klt germs. No completed machine or human check of the full argument is documented here.

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, prior-work, and scoped checking review for non-notifying local inclusion.

Read this published revision