A Counterexample to Nivat's Conjecture for a Non-Convex Window
The paper constructs an exact cluster of cardinality 8 with full affine span and an -tiling whose orbit closure contains no 1-periodic -tiling, giving a non-degenerate counterexample to Nivat's conjecture for non-convex windows. This answers negatively a question of Kari and Moutot from 2023.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Symbolic Dynamics, Tilings
- Posed by
- Maurice Nivat; the specific question by Jarkko Kari and Etienne Moutot
- Year posed
- 2023
- Years open
- 3y
- Solved
- 2026-07-10
- Model
- GPT-5 + Claude Opus 4
- Vendor
- —
- Collaborators
- Abhishek Khetan
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 25 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The paper's note on the use of AI credits the construction of Section 2 - the cluster and tiling that constitute the counterexample - to GPT-5, alongside use of Claude Opus 4.
Verification
No independent review. The object is an explicit finite cluster with an explicit tiling, so the construction can be checked directly. Preprint, not refereed.