chore: paper patches.

Signed-off-by: Amlal El Mahrouss <amlal@nekernel.org>

2 files changed, 202 insertions, 3 deletions

diff --git a/source/wg03/articles/article.tex b/source/wg03/articles/article.tex
index 2b6acb3..12576fc 100644
--- a/source/wg03/articles/article.tex
+++ b/source/wg03/articles/article.tex
@@ -165,7 +165,7 @@
 }]
 
 %% ============================================================
-\section{Denoting CL Execution}
+\section{Introduction}
 \label{sec:cl-introduction}
 
 We propose the following approach to represent the CL execution flow, as execution context a way to mathematically present:
@@ -174,7 +174,7 @@ We propose the following approach to represent the CL execution flow, as executi
 \end{equation}
 Such that an execution context (denoted as $\operatorname{C}$) is a program currently running with rules (denoted as $\operatorname{Trait}(\operatorname{C})$) and domains. We derive the program by its context in this formula, as we depend on $\operatorname{C}$, the $\operatorname{C}$ variable must be valid and computable in a domain $\operatorname{D}$.
 
-\section{Syntax}
+\section{The CL Syntax}
 \label{sec:cl-syntax}
 
 The syntax of a Context Language may consist of traits, and implementations. The traits can be expressed as defined in Nectar. One way to represent it mathematically is:
@@ -187,7 +187,17 @@ Traits and such must be valid in $\operatorname{C} \And$ $\Theta(\operatorname{C
 \section{Example: The Nectar 'CL'}
 \label{sec:cl-example-nectar}
 
-Developing such languages would benefit Software Engineering as we noticed a much faster cycle of software development when using the CL approach rather than the classic CL approach. We also notice that Nectar programs tends to be shorter and more expressive than average.
+Developing such languages would benefit Software Engineering as we noticed a much faster cycle of software development when using the CL approach rather than the classic CL approach.
+\\\\\\\\
+\begin{lstlisting}
+extern palloc; // parallel alloc
+
+const main() {
+  palloc(0, 0, 0);
+  return 0;
+}    
+\end{lstlisting}
+We also notice that Nectar programs tends to be shorter and more expressive than average.
 
 \section{Conclusion}
 \label{sec:cl-conclusion}
diff --git a/source/wg04/articles/article.tex b/source/wg04/articles/article.tex
new file mode 100644
index 0000000..ecbbb4e
--- /dev/null
+++ b/source/wg04/articles/article.tex
@@ -0,0 +1,189 @@
+%% ============================================================
+%% Academic Journal Paper Template
+%% Compatible with: IEEE, ACM, Elsevier, Springer conventions
+%% ============================================================
+
+\documentclass[10pt, twocolumn]{article}
+
+%% ---- Core Packages ----------------------------------------
+\usepackage[T1]{fontenc}
+\usepackage[utf8]{inputenc}
+\usepackage{lmodern}
+\usepackage{microtype}           % Microtypographic refinements
+
+%% ---- Page Geometry ----------------------------------------
+\usepackage[
+  top=1in, bottom=1in,
+  left=0.75in, right=0.75in,
+  columnsep=0.25in
+]{geometry}
+
+%% ---- Mathematics ------------------------------------------
+\usepackage{amsmath, amssymb, amsthm}
+\usepackage{mathtools}
+\usepackage{bm}                  % Bold math symbols
+
+%% ---- Figures & Tables -------------------------------------
+\usepackage{graphicx}
+\usepackage{booktabs}            % Professional table rules
+\usepackage{multirow}
+\usepackage{array}
+\usepackage{caption}
+\usepackage{subcaption}
+\usepackage{float}
+
+%% ---- Algorithms -------------------------------------------
+\usepackage[ruled, vlined, linesnumbered]{algorithm2e}
+
+%% ---- Code Listings ----------------------------------------
+\usepackage{listings}
+\usepackage{xcolor}
+
+\lstdefinestyle{codestyle}{
+  backgroundcolor=\color{gray!8},
+  basicstyle=\ttfamily\footnotesize,
+  breakatwhitespace=false,
+  breaklines=true,
+  captionpos=b,
+  commentstyle=\color{green!50!black},
+  keywordstyle=\color{blue}\bfseries,
+  stringstyle=\color{orange!70!black},
+  numberstyle=\tiny\color{gray},
+  numbers=left,
+  numbersep=5pt,
+  showstringspaces=false,
+  frame=single,
+  rulecolor=\color{gray!40},
+  tabsize=2
+}
+\lstset{style=codestyle}
+
+%% ---- Hyperlinks -------------------------------------------
+\usepackage[
+  colorlinks=true,
+  linkcolor=blue!70!black,
+  citecolor=green!50!black,
+  urlcolor=blue!60!black
+]{hyperref}
+\usepackage{url}
+
+%% ---- Bibliography -----------------------------------------
+\usepackage[numbers, sort&compress]{natbib}
+
+%% ---- Miscellaneous ----------------------------------------
+\usepackage{lipsum}              % Lorem ipsum filler — remove in production
+\usepackage{enumitem}
+\usepackage{siunitx}             % SI units: \SI{3.14}{\mega\hertz}
+\usepackage{cleveref}            % Smart cross-references: \cref{fig:foo}
+
+%% ---- Theorem Environments ---------------------------------
+\theoremstyle{plain}
+\newtheorem{theorem}{Theorem}[section]
+\newtheorem{lemma}[theorem]{Lemma}
+\newtheorem{corollary}[theorem]{Corollary}
+\newtheorem{proposition}[theorem]{Proposition}
+
+\theoremstyle{definition}
+\newtheorem{definition}[theorem]{Definition}
+\newtheorem{example}[theorem]{Example}
+
+\theoremstyle{remark}
+\newtheorem{remark}[theorem]{Remark}
+
+%% ---- Custom Commands --------------------------------------
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\N}{\mathbb{N}}
+\newcommand{\Z}{\mathbb{Z}}
+\newcommand{\E}{\mathbb{E}}
+\newcommand{\Prob}{\mathbb{P}}
+\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}
+\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}
+\newcommand{\inner}[2]{\left\langle #1,\, #2 \right\rangle}
+\newcommand{\ie}{\textit{i.e.}\xspace}
+\newcommand{\eg}{\textit{e.g.}\xspace}
+\newcommand{\etal}{\textit{et al.}\xspace}
+
+%% ---- Caption Formatting -----------------------------------
+\captionsetup{
+  font=small,
+  labelfont=bf,
+  format=hang,
+  justification=justified
+}
+
+%% ---- Header / Footer --------------------------------------
+\usepackage{fancyhdr}
+\pagestyle{fancy}
+\fancyhf{}
+\fancyhead[L]{\small\itshape Ne.org, Vol.~2, No.~1, March 2026}
+\fancyhead[R]{\small\thepage}
+\renewcommand{\headrulewidth}{0.4pt}
+
+%% ============================================================
+%%  FRONT MATTER
+%% ============================================================
+
+\title{%
+  \vspace{-1.5em}%
+  \large\textbf{All you need is Integrals for Debugging.}%
+}
+
+\author{%
+  \textbf{Amlal El Mahrouss}$^{1}$\thanks{Corresponding author. Email: amlal@nekernel.org}
+  \\amlal@nekernel.org, amlalelmahrouss@icloud.com\\[0.4em]
+  \small $^{1}$Ne.org Journal
+}
+
+\date{%
+  \small 3 March 2026
+}
+
+%% ============================================================
+\begin{document}
+
+
+\twocolumn[{%
+  \maketitle
+  \vspace{-0.5em}
+  \rule{\linewidth}{0.4pt}
+  %% ---- Abstract -------------------------------------------
+  \begin{center}
+  \begin{minipage}{0.92\linewidth}
+    \small
+    \textbf{Abstract.}\enspace
+    This development presents an approach of software debugging[1] in which we'll name 'Integrals of Debuggging' (ID).
+    We propose a mathematical of which integrals are used to analyze, modify, and apply, software patches to programs.
+
+    
+    \medskip
+    \textbf{Keywords:}\enspace
+    Computer Science; Mathematics;
+  \end{minipage}
+  \end{center}
+  \vspace{0.8em}
+  \rule{\linewidth}{0.4pt}
+  \vspace{1em}
+}]
+
+\section{Introduction}
+\label{sec:cl-example-integrals}
+
+Let an integral of $\operatorname{LongReturn(x, t)}$ be:
+
+\begin{equation}
+    \operatorname{LongReturn(x, t)} \coloneqq \int_{n}^{p} \operatorname{FastReturn(x, t)} \cdot d\operatorname{t}
+\end{equation}
+Such that $x$ and $t$ are always greater or equal than one, $\operatorname{LongReturn(x, t)}$ shall always be greater than $\operatorname{FastReturn(x, t)}$ for all such value in $\mathbb{R}$.
+This introduction of the LongReturn, will let us jump to our next section about its applications in Computer Analysis.
+
+\section{Constraints}
+
+However before starting, we shall provide the following conditions:
+\begin{equation}
+    \operatorname{LongReturn(x)} \geq \operatorname{FastReturn(x)}, \quad \operatorname{x} \geq 1
+\end{equation}
+The variable x shall also be defined in $\mathbb{R}$ throughout the integral. We shall now proceed into the next section.
+
+\section{Applications in Software Debugging}
+
+\end{document}