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% LaTeX template for mathematical articles
%
% skip to line 216 to start your document
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\documentclass{article}
%\documentclass[11pt,reqno]{amsart}
%\usepackage[tp=1.25in,bottom=1.25in,left=1in,right=1in]{geometry}
\usepackage{amsfonts, amsmath, amssymb, amscd, amsthm, graphicx, mathtools,xfrac}
%\usepackage{enumitem,xfrac}
%\usepackage[final, % change to final 
%colorlinks=true]{hyperref}
%\usepackage[all,cmtip]{xy}

\DeclareRobustCommand{\SkipTocEntry}[5]{}

\usepackage{csquotes}
\MakeOuterQuote{"} 
 
% tikz
%\usetikzlibrary{matrix,arrows,decorations.pathmorphing,patterns}

\usepackage{pgfplots}
\usepackage{tikz,tikz-cd,amscd}
\usetikzlibrary{calc}
\usepackage{mathdots,color}
\usetikzlibrary{decorations.pathreplacing,decorations.markings}
\usetikzlibrary{shapes,shapes.arrows,positioning}

\tikzset{->-/.style={decoration={
  markings,
  mark=at position #1 with {\arrow{>}}},postaction={decorate}}}
\tikzset{->-/.default=.5}

\newcounter{alphathm}

% theorem environments
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}
\newtheorem{alphathm}[alphathm]{Theorem}
\newtheorem{assumption}[theorem]{Standing assumption}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{claim}[theorem]{Claim}
\newtheorem*{claim*}{Claim}

\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{example}[theorem]{Example}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{question}[theorem]{Question}
\newtheorem{convention}[theorem]{Convention}
\newtheorem{remark-convention}[theorem]{Remark-Convention}

\numberwithin{equation}{section}
\numberwithin{theorem}{section}

\renewcommand*{\thealphathm}{\Alph{alphathm}}

\newcommand{\fakeenv}{} %%% prints the emptystring

%%% For theorem style
\newenvironment{restate}[2]  %%% restate takes two arguments 
{ 
 \renewcommand{\fakeenv}{#2} %%% So now \fakeenv prints #2
 \theoremstyle{plain} 
 \newtheorem*{\fakeenv}{#1~\ref{#2}} %%% so now #2 is the name of a
                                     %%% theorem-like environment.   
 \begin{\fakeenv}
}
{
 \end{\fakeenv}
}

% fonts

\newcommand{\bF}{\mathbb{F}}

\newcommand{\HH}{\mathbb{H}} 
\newcommand{\NN}{\mathbb{N}} 
\newcommand{\RR}{\mathbb{R}}
\newcommand{\PP}{\mathbb{P}}
\newcommand{\ZZ}{\mathbb{Z}} 

\newcommand{\calA}{\mathcal{A}}
\newcommand{\calB}{\mathcal{B}}
\newcommand{\calC}{\mathcal{C}}
\newcommand{\calD}{\mathcal{D}}
\newcommand{\calE}{\mathcal{E}}
\newcommand{\calF}{\mathcal{F}}
\newcommand{\calG}{\mathcal{G}}
\newcommand{\calH}{\mathcal{H}}
\newcommand{\calJ}{\mathcal{J}}
\newcommand{\calL}{\mathcal{L}}
\newcommand{\calM}{\mathcal{M}}
\newcommand{\calN}{\mathcal{N}}
\newcommand{\calO}{\mathcal{O}}
\newcommand{\calP}{\mathcal{P}}
\newcommand{\calQ}{\mathcal{Q}}
\newcommand{\calS}{\mathcal{S}}
\newcommand{\calT}{\mathcal{T}}
\newcommand{\calV}{\mathcal{V}}
\newcommand{\calX}{\mathcal{X}}
\newcommand{\calZ}{\mathcal{Z}}

\newcommand{\frakg}{\mathfrak{g}}

\newcommand{\balpha}{{\boldsymbol \alpha}}  
\newcommand{\bbeta}{{\boldsymbol \beta}}  
\newcommand{\bgamma}{{\boldsymbol \gamma}}  
\newcommand{\bxi}{{\boldsymbol \xi}}  

\newcommand{\he}{\hat{e}}
\newcommand{\hv}{\hat{v}}
\newcommand{\hw}{\hat{w}}

\newcommand{\oT}{\overline{T}}
\newcommand{\oY}{\overline{Y}}

\newcommand{\hDelta}{\widehat \Delta}
\newcommand{\hA}{\widehat A}
\newcommand{\hT}{\widehat T}
\newcommand{\hU}{\widehat U}
\newcommand{\hV}{\widehat V}
\newcommand{\hX}{\widehat X}
\newcommand{\hY}{\widehat Y}
\newcommand{\hZ}{\widehat Z}

\newcommand{\sfV}{\mathsf{V}}

\newcommand{\talpha}{{\widetilde \alpha}}
\newcommand{\tbeta}{{\widetilde \beta}}
\newcommand{\tgamma}{{\widetilde \gamma}}
\newcommand{\tsigma}{{\widetilde \sigma}}
\newcommand{\txi}{{\widetilde \xi}}
\newcommand{\tSigma}{{\widetilde \Sigma}}
\newcommand{\ttau}{{\widetilde \tau}}  
  
\newcommand{\ta}{{\widetilde a}}
\newcommand{\tb}{{\widetilde b}}
\newcommand{\te}{{\widetilde e}}
\newcommand{\tv}{{\widetilde v}}
\newcommand{\tA}{{\widetilde A}}
\newcommand{\tC}{{\widetilde C}}
\newcommand{\tD}{{\widetilde D}}
\newcommand{\tM}{{\widetilde M}}
\newcommand{\tN}{{\widetilde N}}
\newcommand{\tT}{{\widetilde T}}
\newcommand{\tU}{{\widetilde U}}
\newcommand{\tX}{{\widetilde X}}
\newcommand{\tY}{{\widetilde Y}}
    
% shortcuts

\newcommand{\norm}[1]{\left\| {#1} \right\|} 
\newcommand{\abs}[1]{\left\lvert {#1} \right\rvert} 
\newcommand{\wght}[1]{\lvert {#1} \rvert} 
\newcommand{\I}[1]{\langle #1 \rangle}
\newcommand{\bd}{\partial}
\newcommand{\from}{\colon\thinspace}
\newcommand{\inject}{\hookrightarrow}
\newcommand{\inv}{^{-1}}
\newcommand{\pmone}{\ensuremath{\{\pm 1\}}}
\newcommand{\surject}{\twoheadrightarrow}

\newcommand{\GP}[2]{\left( #1 \, . \, #2 \right)}

\newcommand{\FN}{F_{N}}
\newcommand{\dsym}{d^{\rm \, sym}}

\newcommand{\margin}[1]{\marginpar{\scriptsize #1}}

\newcommand{\dbtilde}[1]{\widetilde{\raisebox{0pt}[0.85\height]{$\widetilde{#1}$}}}

\newcommand{\vsub}{\rotatebox[origin=c]{-90}{$\subseteq$}}

% complexes

\newcommand{\FF}{\mathrm{FF}}
\newcommand{\ZF}{\mathcal{Z}\mathrm{F}}
\newcommand{\coS}{\mathrm{CoS(\FN)}}

%------
% Don't mess with this unless you know what you're doing.
% (It creates a squarish vertically centered dot that can be used to
%  indicate a free parameter.)
    
\newcommand{\param}%
	{{\mathchoice{\mkern1mu\mbox{\raise2.2pt\hbox{$\centerdot$}}\mkern1mu}%
	{\mkern1mu\mbox{\raise2.2pt\hbox{$\centerdot$}}\mkern1mu}%
	{\mkern1.5mu\centerdot\mkern1.5mu}{\mkern1.5mu\centerdot\mkern1.5mu}}}

%------

% math operators

\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\CV}{CV}
\DeclareMathOperator{\Inc}{Inc}
\DeclareMathOperator{\Inn}{Inn}
\DeclareMathOperator{\Isom}{Isom}
\DeclareMathOperator{\Mon}{Mon}
\DeclareMathOperator{\Out}{Out}
\DeclareMathOperator{\Stab}{Stab}
\DeclareMathOperator{\Sys}{Sys}
\DeclareMathOperator{\Teich}{Teich}
\DeclareMathOperator{\Wh}{Wh}
\DeclareMathOperator{\val}{val}
\DeclareMathOperator{\Mod}{Mod}

\begin{document}

\title{Title of the Article}
\author{Author Name}
\date{\today}   
\maketitle
\begin{abstract}
This is the abstract of the article.
\end{abstract}
\section{Introduction}
This is the introduction section of the article.
\section{Main Results}
This section contains the main results.
\begin{theorem}\label{thm:main}
This is the main theorem.
\end{theorem}
\begin{proof}
This is the proof of the main theorem.
\end{proof}
\section{Conclusion}
This is the conclusion of the article. We cite \cite{Stillwell}.
\bibliographystyle{plain}
\bibliography{references}


% To compile the document, use the following commands:
%  pdflatex main
%  bibtex main
%  pdflatex main
%  pdflatex main
%
% where main.tex is the name of this file and main.bib is the name of your BibTeX file.

\end{document}
