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\hypersetup{pdftitle={Algebraicity of rank-two scattering wall functions},pdfauthor={Qiyue Tang}}
\title{Algebraicity of rank-two scattering wall functions}
\author{Qiyue Tang}
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\footnotetext{\textit{2020 Mathematics Subject Classification.} Primary 13F60; Secondary 05A15, 13F25.\newline
\textit{Keywords.} Tropical vertex group, scattering diagram, algebraic power series, tight grading, catalytic variable.}
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\begin{abstract}
We prove that every wall function in the rank-two scattering factorization determined by two polynomial initial walls over a field of characteristic zero is algebraic. This resolves the algebraicity question posed by Kontsevich and recorded by Gross and Pandharipande, and its cluster-scattering formulation in the work of Burcroff, Lee, Mou, Musiker, and Reineke.
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\section*{AI use and scholarly credit}
The main results and their proof were developed during a two-hour research conversation with ChatGPT-6-Pro. The research materials were subsequently subjected to an adversarial AI review in Codex. The manuscript also passed review by Rethlas-OSV~\cite{RethlasOSV}, using OSVerify~\cite{OSVerify}.

By posting this manuscript on this platform, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in preparing a finished account or checking the arguments; the eventual scholarly credit should go to those who undertake that work.
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\noindent\textsc{Zhili College, Tsinghua University, Beijing 100084, China}\par
\noindent\textit{Email address:}\enspace
\mbox{\href{mailto:tangqy24@mails.tsinghua.edu.cn}{\texttt{tangqy24@mails.tsinghua.edu.cn}}}\par
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