Completeness of Canonical Closure Representations Is coNP-Complete
A finite closure system can be given by implications or by a list of subsets closed under intersection. Deciding whether one specification of each kind defines the same family had remained open in several settings; the paper proves the problem coNP-complete.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Computational Complexity, Closure Systems
- Posed by
- Open in the closure-systems literature
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-20
- Model
- GPT-5.6 Pro
- Vendor
- OpenAI
- Collaborators
- Mikhail Babin
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The disclosure states the main proof was obtained by GPT-5.6 Pro through ChatGPT and checked by the author.
Verification
No independent review; the author reports checking the model's proof himself. Preprint, not refereed.