Minimal models and Mori fibre spaces for generalized log canonical Q-pairs

OpenAI

For projective generalized log-canonical Q-pairs over an algebraically closed characteristic-zero field with a fixed nef rational b-divisor, the manuscript claims a birational model that extracts no divisors and preserves discrepancy inequalities, with nef adjoint when pseudo-effective, or a relative-Picard-number-one Mori fibre space otherwise.

Sources for this record

What was already known

BCHM covered big klt settings. Earlier generalized-pair MMP and transfer results left further smooth relative inputs to establish.

AI involvement AI-led

OpenAI credits an internal model with the manuscript and proof. No named human proof checker or explanation is documented.

The cited release credits an internal OpenAI model with producing the result and the manuscript credits OpenAI as author; the record does not establish model autonomy from task selection or human direction.

Importance Major

This would settle a broad existence problem for generalized lc rational pairs in all dimensions.

Limitations

The claim is existence of a terminating choice, not termination of every MMP, semiampleness, Q-factoriality or real coefficients. No completed check of the local-phase and infinite-program argument is documented.

Technical verification Reported

The cited proof and its cited transfer results are available, but no completed human proof check, machine check or exact certificate check of this theorem is documented. The registry’s statement comparison is not a proof review.

Human understanding Few

No named person explains the central argument in the reviewed sources. Few is the evidence default, not a finding that people cannot understand it.

Correction and publication history

2026-10-18 · publication

If correct, this would settle a broad existence problem for generalized lc rational pairs in all dimensions.

Read this published revision