ProbXiv
sign in
Problem archiveProblem record

A Counterexample to Nivat's Conjecture for a Non-Convex Window

Combinatorics · posed by Maurice Nivat; the specific question by Jarkko Kari and Etienne Moutot, 2023 · disproved

1 comment

Statement

The paper constructs an exact cluster F⊆Z2F\subseteq\mathbb{Z}^2 of cardinality 8 with full affine span and an FF-tiling whose orbit closure contains no 1-periodic FF-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.

Record

Source
Added

Comments

No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Abhishek Khetan, using GPT-5 + Claude Opus 4

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    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.

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.