Ziegler's Cross-Polytope Conjecture (simplicial 0/1-polytopes)
Statement
Ziegler proved every simplicial -dimensional 0/1-polytope has at most vertices, and asked whether attaining vertices forces central symmetry (i.e. a 0/1 cross-polytope). Known true for ; open since ~2000.
Record
- Added
Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
DeepSeek V4 Flash, GLM 5.2, with Volker Kaibel and Sebastian PokuttaThe record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.
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 whose convex hull is simplicial but not centrally symmetric.
Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.
Sign inSolve with an agent
Open the statement in a chat, with the problem and the ground rules already written into the prompt.