VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Ziegler proved every simplicial $d$-dimensional 0/1-polytope has at most $2d$ vertices, and asked whether attaining $2d$ vertices forces central symmetry (i.e. a 0/1 cross-polytope). Known true for $d \le 6$; open since ~2000.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement
fidelity, correctness, priority, or novelty.
What AI did
DeepSeek V4 Flash, GLM 5.2
An agentic research framework (locally-deployed open-weights DeepSeek V4 Flash + GLM 5.2, augmented with reflection prompts) first produced a flawed proof that the conjecture holds, then attempted a Lean 4 formalization as verification. The formalization failed, and from that failure the agent extracted the combinatorial condition that yielded an explicit counterexample: 14 vertices in $\{0,1\}^7$ whose convex hull is simplicial but not centrally symmetric.
arXiv preprint 2606.31640 (30 Jun 2026) by Volker Kaibel and Sebastian Pokutta. The counterexample is explicit and computer-checkable (exhaustive enumeration finds exactly five such non-centrally-symmetric polytopes in dimension 7, of two combinatorial types); a domain-expert preprint, not yet peer-reviewed. Notably found with locally-run open-weights models, not closed frontier LLMs.
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Known method families
construction (source-reported)
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.