Declarations on the use of AI

Suggested template of declaration.

Declaration on the use of AI. The author used [tool] to [check language / assist with literature search / suggest a proof strategy for Lemma 3.2]. All content was reviewed and verified by the author, who takes full responsibility for the paper.

List of sample declarations:

Declaration on the use of AI. The paper is entirely written by the humans. No LLM models were used.

Declaration on the use of AI. Artificial intelligence was not used for the mathematics, writing, computation, or any other part of this paper.

Declaration on the use of AI. No AI was used in the research or writing of this paper.

Declaration on the use of AI. The paper is written by the authors. LLM models were used for final proofread and grammar checking.

Declaration on the use of AI.  An LLM was used to produce (reference list, figure *) and to assist with language editing and polishing the text.

Declaration on the use of AI. An LLM was used to produce (proof of…, example…, etc) and to assist with language editing and polishing the text. The authors have checked all mathematical arguments and take responsibility for all results and arguments.

Declaration on the use of AI. Most results of this paper were found in interactions with LLMs. The writing was done by the author without assistance, with an LLM only used for proofreading.

Declaration on the use of AI. The final paper is human written, using parts of the AI generated proofs, and also proofread by AI. The authors have checked all mathematical arguments and the full text, and take responsibility for all results and arguments presented in this paper.

Declaration on the use of AI. The author used ( name of the LLM ) to search references and discuss proof strategy in this work. The paper is written by the author, who verified all arguments and references, and takes full responsibility for the content.

Declaration on the use of AI. The authors used (name of LLM) as research-assistance tools during the preparation of this manuscript. This paper is fully written by the authors, who take full responsibility for the accuracy and the content of this paper.

Declaration on the use of AI. Large language models were used to (…..). The authors have checked all mathematical arguments and the full text, and take responsibility for all results and arguments presented in this paper.

Declaration on the use of AI. During the preparation of this work, the authors used (name of LLM) as a tool for exploring proof strategies, refining arguments, and drafting and revising the manuscript. All mathematical results and the final text were verified by the author, who take full responsibility for the content of this paper.

Declaration on the use of AI. The proofs outside Section 5 were developed through discussions between the author and (name of LLM) . The proofs in Section 5 were developed primarily by (name of LLM) through interactions with the author. The author has verified the correctness and take full responsibility for the accuracy and the content of this paper.

Updated: 10 October 2026