\documentclass[11pt]{article} \usepackage[a4paper,margin=27mm]{geometry} \usepackage[T1]{fontenc} \usepackage{lmodern} \usepackage{amsmath,amssymb,amsthm,mathtools,booktabs} \usepackage[shortlabels]{enumitem} \usepackage[colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue]{hyperref} \numberwithin{equation}{section} \newtheorem{theorem}{Theorem}[section] \newtheorem{proposition}[theorem]{Proposition} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{maintheorem}{Theorem} \renewcommand{\themaintheorem}{\Alph{maintheorem}} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \newtheorem{example}[theorem]{Example} \newcommand{\dd}{\,\mathrm d} \newcommand{\RR}{\mathbb R} \newcommand{\CC}{\mathbb C} \newcommand{\QQ}{\mathbb Q} \newcommand{\ZZ}{\mathbb Z} \newcommand{\NN}{\mathbb Z_{\geq0}} \newcommand{\HH}{\mathbb H} \newcommand{\vac}{\mathrm{vac}} \newcommand{\one}{\mathbf 1} \newcommand{\rhoF}{\rho^{\mathrm F}} \newcommand{\ev}[1]{#1^{\natural}} \DeclareMathOperator{\supp}{supp} \DeclareMathOperator{\dist}{dist} \DeclareMathOperator{\sinc}{sinc} \setlength{\emergencystretch}{3em} \newcommand{\papercontributor}{Tzu-Chen Huang} \title{Integral torus partition functions just above $c=1$\\ have no fixed spectral gap} \author{\papercontributor} \date{November 2026} \hypersetup{pdftitle={Integral torus partition functions just above c=1 have no fixed spectral gap},pdfauthor={\papercontributor}} \begin{document} \maketitle \input{sections/abstract} \tableofcontents \input{sections/introduction} \input{sections/setup} \input{sections/classification} \input{sections/rigidity} \input{sections/kernels} \input{sections/collision} \input{sections/effective} \input{sections/statement} \input{sections/bibliography} \end{document}