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%% ============================================================
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\fancyhead[L]{\small\itshape Ne.org, Vol.~2, No.~1, March 2026}
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%% ============================================================
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\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
}
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\begin{center}
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\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;
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\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}
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