\documentclass[11pt]{article} \usepackage[T1]{fontenc} \usepackage[type1]{newpxtext} \usepackage{amsmath,amsthm} \usepackage{newpxmath} \usepackage[letterpaper,textwidth=5.4in,textheight=8.6in,left=0.85in,marginparsep=0.18in,marginparwidth=1.25in]{geometry} \PassOptionsToPackage{noadjust}{marginnote}% notes add no height or depth to the text line \usepackage{xcolor,marginnote,microtype,graphicx,caption} \usepackage[super,sort&compress]{natbib} \usepackage[hidelinks,bookmarksnumbered]{hyperref} \hypersetup{pdftitle={On the local geometry of the tight 39-point code in the octonionic projective plane},pdfauthor={Robert R. MacGregor}} \setlength{\emergencystretch}{2em} \captionsetup{font=small,hypcap=false} \newenvironment{conceptfigure}{\begin{figure}[htbp]\centering}{\end{figure}} \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \newif\ifleanrail\leanrailtrue \newcommand{\leannote}[3]{\ifleanrail\marginnote{\raggedright\normalfont\footnotesize\ttfamily\color[gray]{0.35}\href{https://github.com/macgregor-sudo/tight-39-code/blob/46f01c135aacea9003435e7f1dc99b4a69568e83/#2\#L#3}{Lean: #1}}\fi} \title{On the local geometry of the tight 39-point code\\in the octonionic projective plane} \author{Robert R. MacGregor} \date{November 2026} \makeatletter\renewcommand\@biblabel[1]{#1.}\makeatother \begin{document} \begingroup \setlength{\fboxsep}{6pt}\setlength{\fboxrule}{0.4pt} \noindent\fbox{\parbox{\dimexpr\linewidth-2\fboxsep-2\fboxrule\relax}{\small AI Disclaimer: Except for this statement, all content herein was generated by AI.}} \par\endgroup \begingroup \let\newpage\relax \maketitle \endgroup \input{sections/00-abstract} \input{sections/01-introduction} \input{sections/01b-outline} \input{sections/02-codes} \input{sections/03-families} \input{sections/04-linear} \input{sections/05-exhaustion} \input{sections/06-estimates} \input{sections/07-quotient} \input{sections/08-verification} \appendix \input{sections/A-coordinates} \input{sections/B-fourier} \input{sections/C-quadrics} {\small\input{references}} \end{document}