\documentclass[11pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{lmodern} \usepackage[a4paper,margin=30mm]{geometry} \usepackage{amsmath,amssymb,amsthm,mathtools} \usepackage{enumitem,microtype,xurl,xcolor,needspace,booktabs} \usepackage[font=small,labelfont=bf]{caption} \usepackage{tikz} \usetikzlibrary{arrows.meta,calc,positioning,backgrounds,fit,shapes.geometric} \input{figures/styles} \usepackage[hidelinks]{hyperref} \hypersetup{ pdftitle={A characterization of cut-percolating bigraphs}, pdfauthor={Václav Rozhoň}, pdfkeywords={graph norms, cut-percolation, reflection groups, graph isomorphism, designs}, pdflang={en-US} } \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{remark}[theorem]{Remark} \newtheorem{example}[theorem]{Example} \newcommand{\Fix}{\operatorname{Fix}} \newcommand{\Stab}{\operatorname{Stab}} \newcommand{\Aut}{\operatorname{Aut}} \newcommand{\Fold}{\operatorname{Fold}} \newcommand{\RR}{\mathbb R} \newcommand{\EE}{\mathbb E} \newcommand{\Cov}{\operatorname{Cov}} \newcommand{\spec}{\operatorname{spec}} \newcommand{\Sym}{\operatorname{Sym}} \newcommand{\GI}{\mathsf{GI}} \newcommand{\NN}{\mathbb N} \setlist[enumerate]{label=\textup{(\roman*)},leftmargin=*,itemsep=2pt,topsep=4pt} \setcounter{topnumber}{2} \setcounter{bottomnumber}{1} \setcounter{totalnumber}{3} \renewcommand{\topfraction}{.85} \renewcommand{\bottomfraction}{.65} \renewcommand{\textfraction}{.12} \renewcommand{\floatpagefraction}{.75} \setlength{\textfloatsep}{16pt plus 3pt minus 3pt} \setlength{\intextsep}{12pt plus 3pt minus 2pt} \setlength{\emergencystretch}{2em} \makeatletter \renewcommand{\@maketitle}{% \newpage \null \vskip 0pt \begin{center} {\LARGE \@title \par} \ifx\@author\@empty\else \vskip .5em {\large \begin{tabular}[t]{c}\@author\end{tabular}\par} \fi \vskip .5em {\small \@date \par} \end{center} \vskip .4em } \makeatother \title{A characterization of cut-percolating bigraphs\thanks{% All mathematical work was done by GPT-6. The author takes responsibility for the correctness of the paper.}} \author{V\'aclav Rozho\v{n}\\[2pt] {\small Charles University, Prague, Czech Republic}} \date{October 11, 2026} \begin{document} \maketitle \begin{abstract} Conlon and Lee introduced reflection bigraphs and cut-percolation in their study of graph norms. We prove that, for connected bigraphs, these two notions coincide, confirming their prediction. \end{abstract} \input{introduction} \input{preliminaries} \input{structure} \input{recognition} \input{one-sided} \input{discussion} \appendix \input{designs} \input{consequences} \input{local-obstruction} \input{references} \end{document}