Simon's Extendable Shellability Conjecture
Simon conjectured that every skeleton of a simplex is extendably shellable. False: for every there is a pure -dimensional shellable simplicial complex that is not shelling completable.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Combinatorial topology
- Posed by
- Robert Simon
- Year posed
- 1994
- Years open
- 32y
- Solved
- 2026-05-23
- Model
- ChatGPT 5.5
- Vendor
- OpenAI
- Collaborators
- Davide Bolognini, Paolo Sentinelli
- Verification
- Site-confirmed
- Publication
- Preprint
- Significance
- 25 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The paper says the contractible simplicial complex behind the counterexample was identified with the assistance of ChatGPT 5.5, and that the published version reaches the same complex through exhaustive computation.
Verification
The refutation is an explicit finite simplicial complex, reproduced by exhaustive computation in the paper, so it is a finite check. arXiv preprint, not peer-reviewed.
Source
arXiv:2605.24732 - Non-extendably shellable skeleta of simplices