What was already known
Ziegler proved the 2d vertex bound. Prior enumeration supported the characterization through dimension six.
AI involvement
A DeepSeek V4 Flash/GLM 5.2 agent found the antipodal split structure that led to the witness. Kaibel and Pokutta verified and explained the final construction.
The agent supplied the retained antipodal-structure insight leading to the witness; Kaibel and Pokutta framed, checked and wrote the final result.
Importance
Provides a counterexample in the first possible dimension.
Limitations
Two independent exact-rational computations check the explicit witness; the separate enumeration of five symmetry classes is not part of this claim. An earlier failed Lean proof did not check the counterexample.
Technical verification
For this finite explicit witness, the paper reports two independent exact-rational computations of all load-bearing polytope properties, with agreement. The source-reported exact certificate covers the counterexample; the broader five-class enumeration is a separate claim.
Formal checking
Two independent exact-rational implementations check the explicit witness’s dimension, facets, simpliciality and lack of central symmetry.
- Checker
- Two independent exact-rational implementations reported by Kaibel and Pokutta
- Scope
- The fourteen listed 0/1 vertices form a full-dimensional simplicial seven-polytope with 136 facets and without central symmetry
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The named authors explain the balanced-coordinate and split-pair reduction that led to the example, and give a direct geometric account of its missing antipodes and simpliciality.
Correction and publication history
Provides a counterexample in the first possible dimension.
Read this published revision