chore: makefile and paper organization improvements.

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

1 files changed, 0 insertions, 79 deletions

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-% AUTHOR: Amlal El Mahrouss
-% PURPOSE: WG05.TN001: The Mathematics of Execution.
-
-\documentclass[11pt,a4paper]{article}
-
-\usepackage[utf8]{inputenc}
-\usepackage[T1]{fontenc}
-\usepackage{amsmath,amssymb,amsthm}
-\usepackage{hyperref}
-\usepackage[margin=1in]{geometry}
-
-\title{The Mathematics of Execution.}
-\author{Amlal El Mahrouss\\
-\texttt{amlal@nekernel.org}}
-\date{January 2026}
-
-\begin{document}
-
-\bf \maketitle
-
-\begin{center}
-	\rule[0.01cm]{17cm}{0.01cm}
-\end{center}
-
-\begin{center}
-\begin{abstract}
-This paper covers the algebraic properties and concepts of `The Execution Semantics' paper by El Mahrouss, A (2026). It is intended as an additional resource over the aforementioned paper.
-We will define their concepts alongside their properties. We assume the reader has read the previous paper on 'The Execution Semantics' by El Mahrouss, A.
-\end{abstract}
-\end{center}
-
-\begin{center}
-	\rule[1cm]{17cm}{0.01cm}
-\end{center}
-
-\section{The Execution Product}
-
-Let $\Gamma(x, y, z)$ be an execution product of variable arguments $x$, $y$, $z$ defined in compatible and composable execution context $E$: \\
-Let the index $\alpha$ denote the current execution domain of an execution product.
-\\ Let the following formula:
-\begin{equation}
-\Gamma(x, y, z) = \prod_{\alpha=1}^{n}(x_{\alpha} \times y_{\alpha} \times z_{\alpha})+C    
-\end{equation}
- Be defined as the execution product. Where $C$ is the Unknown Execution of $\Gamma(x, y, z)$—now defined as $g(E)$.
-
-\subsection{Properties}
-
-\begin{enumerate}
-
-    \item $\Gamma$ as defined previously as the `execution product' shall always be valid within the execution context $E$.
-    \item The execution context $E$ shall not denote $\varnothing$.
-
-\end{enumerate}
-
-\section{The Unknown Execution}
-
-Let an `Unknown Execution' $U$ be defined regarding an execution product $\Gamma$. \\
-Let $N$ be defined as $\varnothing$.
-
-\subsection{Properties}
-
-\begin{enumerate}
-
-    \item $U$ shall not be equal to $N$.
-    \item The execution domain of $\Gamma$ shall not be $N$.
-
-\end{enumerate}
-
-\section{Conclusion}
-
-Such properties are essential to define `Execution Theory''s as a mathematical construct as per defined in El Mahrouss, A.' paper. 
-
-\section{References}
-
-\begin{enumerate}
-    \item El Mahrouss, A. (2026). The Execution Semantics: On Axioms, Domains, and Authority. (v2.0.0). Zenodo. https://doi.org/10.5281/zenodo.18366611
-\end{enumerate}
-
-\end{document}