OpenAI reports a conditional all-dimensional Kähler log-abundance theorem

Assuming logarithmic Iitaka subadditivity for the specified smooth projective reduced-boundary fibrations, every analytically nef Q-Cartier log canonical divisor K_X+Delta on a normal irreducible compact Kähler space with effective rational boundary is semiample.

Sources for this record

What was already known

Log abundance was known for projective and compact Kähler log canonical threefolds. The manuscript uses the conjectured projective logarithmic Iitaka subadditivity as an explicit input to extend the implication to compact Kähler spaces in arbitrary dimension (manuscript introduction, Context and relation to earlier work, pp. 3–4).

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

If correct under its assumption, reduces all-dimensional compact Kähler log abundance to a specified projective logarithmic subadditivity statement.

Limitations

The main theorem is conditional on logarithmic Iitaka subadditivity; this record does not claim unconditional log abundance.

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