Ehrhart Positivity of Schubitopes

Precise statement

Monical, Tokcan and Yong conjectured that Schubitopes, the generalized permutahedra arising as Newton polytopes of Schubert polynomials and of Demazure characters of $\mathrm{GL}_n$, are Ehrhart positive. Disproved by an explicit Schubitope whose Ehrhart polynomial has a negative coefficient in its monomial expansion.

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

GPT-5.6 Sol Pro

The abstract states the counterexample was found using GPT-5.6 Sol Pro in ChatGPT. The authors supply the surrounding treatment of the family.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

arXiv preprint; not yet peer-reviewed. The result is a single explicit polytope, so it is checkable by direct computation.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-08-01

   arXiv:2608.00377 - Schubitopes are not Ehrhart positive

   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.