%% if you are submitting an initial manuscript then you should have submission as an option here
%% if you are submitting a revised manuscript then you should have revision as an option here
%% otherwise options taken by the article class will be accepted
\documentclass[submission]{FPSAC2027}
%% but DO NOT pass any options (or change anything else anywhere) which alters page size / layout / font size etc

%% note that the class file already loads {amsmath, amsthm, amssymb}

\newtheorem{thm}{Theorem}
\newtheorem{lem}{Lemma}

\usepackage{lipsum}

%% define your title in the usual way
\title[Optional shorter title]{Something to do with math}

%% define your authors in the usual way
%% use \addressmark{1}, \addressmark{2} etc for the institutions, and use \thanks{} for contact details
%% for more than 3 names, use the Oxford comma: One Author, Two Author, Red Author, \and Blue Author
\author[Optional shorter names]{Longer names me\thanks{\href{mailto:hello@world.c}{hello@world.c}. Longer names me was partially supported by Grant 2017.11.14.$\partial$\;supp.}\addressmark{1} \and you\addressmark{2}}

%% then use \addressmark to match authors to institutions here
\address{\addressmark{1}Department of This, University of That, There \\ \addressmark{2}School of Something, University of Something Else, Somewhere}

%% put the date of submission here
\received{\today}

%% leave this blank until submitting a revised version
%\revised{}

%% put your English abstract here, or comment this out if you don't have one yet
%% please don't use custom commands in your abstract / resume, as these will be displayed online
%% likewise for citations -- please don't use \cite, and instead write out your citation as something like (author year)
\abstract{\lipsum[1]}

%% put your French abstract here, or comment this out if you don't have one
\resume{\lipsum[2]}

%% put your keywords here, or comment this out if you don't have them yet
\keywords{math, maths, mathematics}

%% you can include your bibliography however you want, but using an external .bib file is STRONGLY RECOMMENDED and will make the editor's life much easier
%% regardless of how you do it, please use numerical citations; i.e., [xx, yy] in the text

%% this sample uses biblatex, which (among other things) takes care of URLs in a more flexible way than bibtex
%% but you can use bibtex if you want
\usepackage[backend=bibtex]{biblatex}
\addbibresource{sample.bib}
%% note the \printbibliography command at the end of the file which goes with these biblatex commands

\begin{document}

\maketitle
%% note that you DO NOT have to put your abstract here -- it is generated by \maketitle and the \abstract and \resume commands above

\section{A section}

\lipsum[3]

\begin{equation}\label{eqn:eq1}
\int_0^\infty \exp(-x) \, \mathrm{d}x = 1.
\end{equation}

\begin{lem}\label{lem:lem1}
\lipsum[11]
\end{lem}

\lipsum[10]

\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{plot}
\caption{A plot of a function.}
\label{fig:plot}
\end{figure}

\subsection{A subsection}

\lipsum[5]

\begin{align*}
1 + 1 + 1 &= 2 + 1 \\ &= 3.
\end{align*}

\subsubsection{A subsubsection}

\lipsum[17]

Here is a citation~\cite{greenwade93} with URL. Here is another
citation~\cite{MR4}, which is the earliest-numbered Math Review with a
functioning DOI: MR0000004. Finally, a reference to
equation~\eqref{eqn:eq1}. And a reference to Figure~\ref{fig:plot}.

\acknowledgements{\lipsum[20]}

%% if you use biblatex then this generates the bibliography
%% if you use some other method then remove this and do it your own way
\printbibliography


\clearpage
\section*{AI disclosure}

Please include a statement describing the use of AI tools in this work. In particular, indicate whether AI tools were used for exploration, brainstorming, coding, computation, mathematical reasoning, proving, writing, generating figures, proofreading, or any other aspect of the work. Please also specify the AI tools and models used. There is no length limit for this section, and it does not count toward the 12-page limit. The following examples illustrate the expected level of detail:
\begin{itemize}
	\item about mathematical content:
	\begin{itemize}
		\item Lemma 3, including both its statement and its proof, was suggested by ChatGPT (GPT 5.6 Sol Pro). The authors subsequently checked the proof independently and revised its exposition.
		\item Claude (Opus 5) was used to explore possible approaches to Theorem 7. In particular, it suggested the reduction to Proposition 6, while the subsequent argument was developed by the authors.
		\item The bijection used in the proof of Theorem 6 was suggested by ChatGPT (GPT-5.6 Luna). The authors formalized the construction and verified that it is indeed a bijection.
		\item The authors used an AI tool (Claude Fable 5.1) as an exploratory mathematical collaborator throughout Section 3. In particular, it suggested Conjecture 5, found the counterexample in Example 6, and proposed the strengthening of Lemma 7 that ultimately led to Theorem 8.
		\item The main theorem of the paper originated from an AI-assisted exploration (using GPT-6 Astra). After being given the definitions and several small examples, ChatGPT proposed the statement of Theorem 1 and suggested the induction on which the eventual proof is based. The authors subsequently developed, verified, and wrote the complete proof.
		\item The proof of Theorem 4 was obtained by prompting an AI tool (Claude Fable 5.1) with the statement of the problem and asking it to find a proof; the resulting argument was then verified and reformulated by the authors.
	\end{itemize}
	\item about exposition:
	\begin{itemize}
		\item ChatGPT (GPT-5.6 Luna) was used only for proofreading and improving the English throughout the manuscript.
		\item Claude Fable 5.1 was used to improve the exposition of Definition 5 but the mathematical content was unchanged.
		\item AI tools (Claude Opus 5) were used to suggest alternative formulations of Definition 5. The final formulation was selected and verified by the authors.
	\end{itemize}
	\item about code and experiments:
	\begin{itemize}
		\item The SageMath code used for the computations in Section 4 was initially generated by an AI tool (Claude Opus 5) and subsequently tested and modified by the authors.
		\item ChatGPT (GPT-5.6 Luna) was used to optimize the code underlying Table 2, but not to design the algorithm or interpret the resulting data.
		\item Claude Opus 5 was used to generate computational data for \(n\leq 9\), which led the authors to formulate Conjecture 4.
		\item ChatGPT (GPT-5.6 Luna) was used to search for potential counterexamples to Conjecture 9 and identified the example presented in Example 10.
	\end{itemize}
	\item about figures:
	\begin{itemize}
		\item Figure 3 was generated with the assistance of an AI tool (GPT-5.6 Luna) from specifications provided by the authors.
		\item Figure 2 was generated entirely by an AI tool (Claude Opus 5) from a textual description provided by the authors.
		\item The authors provided the mathematical content of Figure 3, while its graphical layout and visual design were generated by ChatGPT (GPT-5.6 Luna).
	\end{itemize}
\end{itemize}
 

\end{document}