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\title{An exact computer-assisted certificate for\\ \(R(5,6)\leq84\)\\[8pt]\large Article and explanatory supplements}
\author{András Pongrácz\\ University of Debrecen, Institute of Mathematics}
\date{30 October 2026}
\begin{document}
\maketitle
\section*{Status and accompanying verification files}
The complete verification archive is available at \url{https://github.com/apongracz86/Ramsey56/releases/tag/v1.0-review}. 
The three parts reproduce the article, the worked explanation, and the detailed mathematical specification. The archive \path{verification.tar.xz} preserves the verification files and their directory structure. Its SHA-256 digest is
\begin{quote}\small\path{88ded8db2254dec75be80e476d684334a685654e3c5a4108cf9c10422bdd3d67}\end{quote}
File names cited in the three parts refer to that distribution. Its README and the specification give the reproduction recipes. The article states the external mathematical inputs. The specification explains the calculations performed by each verification program.
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\startcomponent{The article}{An exact computer-assisted certificate for\\ \(R(5,6)\leq84\)}
\begin{center}András Pongrácz\\ University of Debrecen, Institute of Mathematics\\[3pt]30 October 2026\end{center}
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\startcomponent{The method and a worked local example}{Reading the exact certificate for \(R(5,6)\leq84\):\\
the method and a worked local example}
\begin{center}Explanatory supplement\\[3pt]29 October 2026\end{center}
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\startcomponent{Detailed mathematical specification}{Detailed mathematical specification of the certificate for\\$R(5,6)\leq84$\\[4pt]Verification recipes and representative calculations}
\begin{center}Supplement to the accompanying manuscript\\[3pt]29 October 2026\end{center}
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\input{specification.tex}
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\end{document}