chore: add new paper for WG04.

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

2 files changed, 77 insertions, 1 deletions

diff --git a/source/README.md b/source/README.md
index ee6a411..ea0d77a 100644
--- a/source/README.md
+++ b/source/README.md
@@ -9,7 +9,7 @@
 - WG01: `The PL/OS Group`.
 - WG02: `The Systems Group`.
 - WG03: `The Nectar PL Group`.
-- WG04-SPACE-RF: `The Distributed Systems Group`.
+- WG04-SPACE-RF: `The Mathematics Group`.
 - WG05: `The Execution Theory Group`.
 
 ## Active Paper Groups:
diff --git a/source/wg04-space-rf/paper.tex b/source/wg04-space-rf/paper.tex
new file mode 100644
index 0000000..a2e5790
--- /dev/null
+++ b/source/wg04-space-rf/paper.tex
@@ -0,0 +1,76 @@
+% AUTHOR: Amlal El Mahrouss
+% PURPOSE: WG04: Integrals and Equations for Analysis.
+
+\documentclass[11pt, a4paper]{article}
+\usepackage{graphicx}
+\usepackage{listings}
+\usepackage{amsmath,amssymb,amsthm}
+\usepackage{xcolor}
+\usepackage{hyperref}
+\usepackage[margin=0.5in,top=1in,bottom=1in]{geometry}
+
+\title{Integrals and Equations for Analysis.}
+\author{Amlal El Mahrouss\\\texttt{amlal@nekernel.org}}
+\date{February 2026}
+
+\definecolor{codegray}{gray}{0.95}
+\definecolor{codeblue}{rgb}{0.1,0.1,0.8}
+\definecolor{codegreen}{rgb}{0,0.6,0}
+\definecolor{codepurple}{rgb}{0.58,0,0.82}
+
+\lstset{
+	language=C++,
+	backgroundcolor=\color{codegray},
+	basicstyle=\footnotesize\ttfamily,
+	keywordstyle=\color{codeblue}\bfseries,
+	commentstyle=\color{codegreen},
+	stringstyle=\color{codepurple},
+	numbers=left,
+	numberstyle=\tiny\color{gray},
+	stepnumber=1,
+	numbersep=5pt,
+	breaklines=true,
+	breakatwhitespace=false,
+	frame=single,
+	rulecolor=\color{black},
+	captionpos=b,
+	keepspaces=true,
+	showspaces=false,
+	showstringspaces=false,
+	showtabs=false,
+	tabsize=2
+}
+
+\begin{document}
+
+\bf \maketitle
+
+\begin{center}
+	\rule[0.01cm]{17cm}{0.01cm}
+\end{center}
+
+\abstract
+{
+	This technical note defines useful integrals to be used in the case of calculus. The formulas have been kept abstract for the sole purpose of flexibility.
+}
+
+\begin{center}
+	\rule[1cm]{17cm}{0.01cm}
+\end{center}
+
+\section{Definitions}
+
+\subsection{Definition of a sum of an integral from $a_{0}$ to $a_{n}$}
+
+Let an integral $\alpha$:
+\begin{equation}
+    \int_{a_{0}}^{a_{n}}\sum_{b_{a_{0}},k=a_{0}} f_{b_{a_{0}}}(S(k+b_{a_{0}})) + C
+\end{equation}
+Such that
+\begin{equation}
+    a = 0, \quad a \in \mathbb{N}, \quad k \neq 0, \quad k \in \mathbb{R}
+\end{equation}
+Such that $S$ is a user-defined function computing a sum of $k-b_{a_{0}}$.
+
+\end{document}
+