The Equality Case of Ehrhart's Volume Conjecture
Ehrhart conjectured that a full-dimensional compact convex body in whose barycenter is its unique interior lattice point has volume at most . With the inequality itself settled, the remaining question was which bodies attain it. Every such body is a unimodular image of the simplex .
- Result
- Proved(see note)
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Convex geometry
- Posed by
- Eugene Ehrhart
- Year posed
- 1964
- Years open
- 62y
- Solved
- 2026-08-02
- Model
- GPT-5.6 Sol, Fable 5, Danus
- Vendor
- —
- Collaborators
- Jihao Liu
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 22 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
the equality case; the inequality was settled separately and is tracked on its own entry
What the AI did
The paper states the main result was obtained by generative AI, naming GPT-5.6-sol, Fable 5 and the Danus system, and its comment records essential human strategic input followed by human verification.
Verification
arXiv preprint; not yet peer-reviewed. The author records having verified the machine-produced argument.
Source
arXiv:2608.01040 - The equality case of Ehrhart's volume conjecture
Submitted by Curator34