Real-Rootedness of Ehrhart h*-Polynomials at Large Width

Precise statement

A question of Averkov, Hofscheier and Nill on whether the Ehrhart $h^*$-polynomial of a lattice polytope of large lattice width is real-rooted. Proved in fixed dimension for sufficiently large lattice width, giving strict log-concavity and unimodality of the $h^*$-vector, with the analogous statement for the local $h^*$-polynomial of a lattice simplex.

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

ChatGPT 5.6 Sol

The acknowledgments state that the proofs were found using ChatGPT 5.6 Sol, which also produced a first draft of the paper, with the author solely responsible for the final version.

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

Verification boundary

unreviewed

arXiv preprint, not yet peer-reviewed.

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

Timeline

1. 2026-08-04

   arXiv:2608.03635 - Lattice polytopes of large width have real-rooted Ehrhart h*-polynomials

   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

argument (source-reported)

Source-reported tools: argument.

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.