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\hypersetup{pdftitle={Residual-dimension obstructions for null-projected supersymmetric Yang-Mills theories},pdfauthor={Deep Bhattacharjee}}

\title[Residual-dimension obstructions for null-projected SYM theories]{Residual-dimension obstructions for null-projected supersymmetric Yang--Mills theories}

\author{Deep Bhattacharjee\,\orcidlink{0000-0003-0466-750X}}
\address{Formerly, Electro-Gravitational Space Propulsion Laboratory (EGSPL), Bhubaneswar, Odisha 751030, India}
\address{Formerly, University of Calcutta, Senate House, 87/1 College Street, Kolkata 700073, West Bengal, India}
\email{d.bhattacharjee@erl-forschung.de}
\email{itsdeep@live.com}
\email{egspl@proton.me}
\thanks{\sloppy Corresponding author: Deep Bhattacharjee. Email: \href{mailto:d.bhattacharjee@erl-forschung.de}{d.bhattacharjee@erl-forschung.de}, \href{mailto:itsdeep@live.com}{itsdeep@live.com}, \href{mailto:egspl@proton.me}{egspl@proton.me}; ORCID \href{https://orcid.org/0000-0003-0466-750X}{0000-0003-0466-750X}.}

\subjclass[2020]{81T60; 81T13, 15A66, 81R25, 83E15}
\keywords{Supersymmetry; Yang--Mills theory; Clifford algebras; spinors; null projections}
\date{28 October 2026}

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\noindent\textbf{Note.} This is the third version of the preprint \href{https://hexagonmath.org/2610.00471v2}{hexagon:2610.00471v2}. Section~\ref{ssec:transfer} is new. It quotes the transfer of Nishino's construction to $(11+8n)+3$ proposed by Rios, Marrani and Chester, writes out what repeating Nishino's proof there requires, and proves that it fails for every rank of the null frame (Proposition~\ref{prop:transfer}); Appendix~\ref{app:transfer} checks each step in explicit gamma matrices. The \LaTeX{} source, numerical programs and verification logs are released at \href{https://github.com/creelie/Paper_4}{github.com/creelie/Paper\_4} (release \texttt{v1.5.0}, archived as \href{https://doi.org/10.5281/zenodo.23744833}{10.5281/zenodo.23744833}); the second version is release \texttt{v1.3.0}, archived as \href{https://doi.org/10.5281/zenodo.23672585}{10.5281/zenodo.23672585}.
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