Termination for projective log canonical fourfolds with rational boundary

OpenAI

For a projective four-dimensional log canonical pair with rational boundary over an algebraically closed characteristic-zero field, every program permitted by Definition 1.1 has finitely many birational steps for every choice of negative extremal ray.

Sources for this record

What was already known

Earlier termination results covered terminal or canonical cases, selected or scaled programs, and lc sequences with extra positivity assumptions.

AI involvement AI-led

OpenAI is the credited author of the model-produced projective manuscript. The general Kähler companions are separate results; the human role in this projective proof is not described.

The projective theorem is in an OpenAI-authored model-output manuscript; the release does not support a stronger autonomy attribution.

Importance Major

Would settle ordinary termination for the stated projective log canonical fourfold programs.

Limitations

The step rules exclude flops, extra blowups and inserted isomorphisms; nef endpoints need not be abundant. No completed check of this proof is documented.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The manuscript supplies a long proof, but neither it nor the reviewed repository materials documents a completed human review, Lean proof, or exact certificate for this projective theorem. Reported is the missing-evidence default.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. The manuscript explains its difficulty and branch estimate, but a human explanation of the central proof is undocumented; this is a missing-evidence default.

Correction and publication history

2026-10-18 · publication

Would settle ordinary termination for the stated projective log canonical fourfold programs.

Read this published revision