Problem detail · source-aware
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Simon conjectured that every skeleton of a simplex is extendably shellable. False: for every $d \ge 3$ there is a pure $d$-dimensional shellable simplicial complex that is not shelling completable.
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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.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
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 arXiv preprint, not peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.