Lassak's Area Bound for Reduced Planar Bodies
Lassak conjectured that a reduced planar convex body of thickness has area at most , the value for the disc. False: an explicit reduced body of thickness has area , given by a closed-form support function.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Construction
- Field
- Convex geometry
- Posed by
- Marek Lassak
- Year posed
- —
- Years open
- —
- Solved
- 2026-06-26
- Model
- GPT-5.5 Pro, Claude Opus 4.8
- Vendor
- OpenAI / Anthropic
- Collaborators
- Scott Duke Kominers
- Verification
- Site-confirmed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The acknowledgement credits the models with assisting the computations and coding in preparing the article, without separating which step came from where, so the lowest tier applies.
Verification
The counterexample is given by an explicit support function with the area stated to six decimal places, so the refutation reduces to evaluating a closed-form integral. Single-author arXiv preprint, not peer-reviewed.
Source
arXiv:2606.28612 - A reduced planar body with area greater than pi/4