diff --git a/ccs-body.tex b/ccs-body.tex
index 54e1551..b24d291 100644
--- a/ccs-body.tex
+++ b/ccs-body.tex
@@ -27,9 +27,11 @@ In this work, we address this important issue and present XX (un petit nom ??),
 We prove that the properties needed to maintain security of the protocol still hold in a dynamic context.
 Our contributions are as follows:
 \begin{itemize}
-  \item Study of the Mining in Logarithmic Space protocol in the variable difficulty setting.
-  \item Modification of the protocol to account for said dynamicity.
-  \item Proof of properties in the dynamic context.
+\item We propose XX, a NIPoPoW protocol that handles a variable PoW difficulty for blocks while operating in $O(\polylog(n))$ storage complexity and $O(\polylog(n))$ communication complexity;
+\item We present experimental results illustrating the compression of Bitcoin. 
+%  \item Study of the Mining in Logarithmic Space protocol in the variable difficulty setting.
+  %\item Modification of the protocol to account for said dynamicity.
+ % \item Proof of properties in the dynamic context.
 \end{itemize}
 
 
@@ -231,7 +233,7 @@ Any scheme for operating and compressing blockchains requires to design (i) a \e
 
 \subsubsection{Chain Compression Algorithm}
 
-The Kiayias et al.'s chain compression algorithm (from~\cite{10.1145/3460120.3484784}, Algorithm 1) is parameterized by a security parameter $m$ and the common prefix parameter $k$. System parameter $m$ represents the number of blocks that a party wishes to receive to feel safe. The algorithm compresses the blockchain except for the $k$ most recent blocks, called \emph{unstable} blocks. The compression works as follows: for the highest level $\ell$ that contains more than $2m$ blocks, keep all the blocks but for every level $\mu$ below $\ell$, only keep the last $2m$ blocks and all the blocks after the $m^\text{th}$ block at the $\mu+1$ level. $\Pi$ is used to represent an instance of NIPoPoW proof. %\sg{what is $\mu$ here?} %\ea{We should introduce the $\Pi$ notation here}
+The Kiayias et al.'s chain compression algorithm (from~\cite{10.1145/3460120.3484784}, Algorithm~\cite{alg:chaincompression}) is parameterized by a security parameter $m$ and the common prefix parameter $k$. System parameter $m$ represents the number of blocks that a party wishes to receive to feel safe. The algorithm compresses the blockchain except for the $k$ most recent blocks, called \emph{unstable} blocks. The compression works as follows: for the highest level $\ell$ that contains more than $2m$ blocks, keep all the blocks but for every level $\mu$ below $\ell$, only keep the last $2m$ blocks and all the blocks after the $m^\text{th}$ block at the $\mu+1$ level. $\Pi$ is used to represent an instance of NIPoPoW proof. %\sg{what is $\mu$ here?} %\ea{We should introduce the $\Pi$ notation here}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \subsubsection{Compressed Chain Comparison Algorithm}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -423,7 +425,7 @@ Given a chain $\mathcal{C}$ we want to compress, we set aside the most recent an
 The remaining $\mathcal{C}[:-k]$ constitutes our stable part of the chain.
 
 \begin{algorithm}
-\caption{Chain compression algorithm.}\label{alg:compression}
+\caption{\label{alg:chaincompression}Chain compression algorithm.}
 \begin{algorithmic}
 \Function{Dissolve$_{m,k}$}{$\mathcal{C}$}
 \State $\mathcal{C}^* \gets \mathcal{C}[:-k]$
@@ -450,7 +452,7 @@ The remaining $\mathcal{C}[:-k]$ constitutes our stable part of the chain.
 \end{algorithm}
 
 \begin{algorithm}
-\caption{State comparison algorithm.}\label{alg:comparison}
+\caption{\label{alg:statecomparison}State comparison algorithm.}
 \begin{algorithmic}
 \Function{maxvalid$_{m,k}$}{$\Pi, \Pi'$}
 \If{$\Pi$ is not valid}
diff --git a/ccs-template.tex b/ccs-template.tex
index d910ad9..f013d57 100644
--- a/ccs-template.tex
+++ b/ccs-template.tex
@@ -44,6 +44,9 @@
 \hidecommentfalse % comment to hide comments
 \newcommand\LM[1]{\ifhidecomment{}\else{\textcolor{blue}{LM: #1}}\fi}
 
+\usepackage{ stmaryrd }
+\newtheorem{theorem}{Theorem}
+\newtheorem{definition}{Definition}
 
 %\fancyhf{} % Remove fancy page headers 
 %\fancyhead[C]{Anonymous submission \#9999 to ACM CCS 2023} % TODO: replace 9999 with your paper number
@@ -59,6 +62,8 @@
 
 \begin{document}
 \title{Mining in Logarithmic Space with Variable Difficulty} % TODO: replace with your title
+\author{}
+\maketitle
 
 \begin{abstract}
     This paper addresses the lack of scalability in current blockchain technology and its hindrance to widespread adoption.
@@ -91,7 +96,6 @@
 
 % \keywords{blockchains; proof-of-work; logspace mining; superlight clients; NIPoPoWs; superblocks; variable difficulty} % TODO: replace with your keywords
 
-\maketitle
 
 \input{ccs-body} % TODO: replace with your brilliant paper!