Termination of projective log-canonical fourfold programs
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For a projective log canonical fourfold pair with rational boundary over an algebraically closed characteristic-zero field, does every minimal model program allowed by the cited Definition 1.1 have only finitely many birational steps? Every choice of negative extremal ray is included.
Why it matters and what counts as progress
Why it matters: Ordinary termination would extend results for selected programs, terminal or canonical singularities, and extra positivity assumptions.
What counts as progress: A finite-step termination proof for every permitted program, without replacing the claim by existence of one terminating choice.
How the problem developed
- 24 Sept 2026 · Termination claim [1]
OpenAI Claimed termination of arbitrary permitted minimal model programs for projective log-canonical fourfolds with rational boundary in characteristic zero.
AI contribution
Termination for projective log canonical fourfolds with rational boundary
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
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Publication dates and editorial changes.
OpenAI reports termination of projective lc fourfold programs