A Counterexample to Nivat's Conjecture for a Non-Convex Window
The paper constructs an exact cluster $F\subseteq\mathbb{Z}^2$ of cardinality 8 with full affine span and an $F$-tiling whose orbit closure contains no 1-periodic $F$-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.
Exact FrontierDelta
Scope and record
Occurred: Jul 10, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: A Counterexample to Nivat's Conjecture for a Non-Convex Window · Nivat, non-convex window
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Abhishek Khetan
human · human collaborator
GPT-5 + Claude Opus 4
model · ai model contributor
Lineage and corrections
This event attributed to Abhishek Khetan
This event attributed to GPT-5 + Claude Opus 4