\usepackage{amsmath,amssymb,amsthm,mathtools,mathrsfs} \usepackage{booktabs} \usepackage{enumitem} \usepackage{needspace} \usepackage{xcolor} \usepackage{graphicx} \usepackage{tikz} \usetikzlibrary{arrows.meta,calc,positioning} \usepackage{hyperref} \usepackage[nameinlink,capitalise,noabbrev]{cleveref} \hypersetup{ hypertexnames=false, hidelinks, pdfauthor={Haoyu Sun}, pdftitle={Phase-Labeled Doubles and Disjoint Handleslide Cubes with Complete Markings} } \numberwithin{equation}{section} \newtheorem{theorem}{Theorem}[section] % Independent citable statements for the two conceptual results. The exact % technical theorem chain and its numbering remain unchanged. \newtheorem{headlinetheorem}{Theorem} \renewcommand{\theheadlinetheorem}{\Alph{headlinetheorem}} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \crefname{equation}{equation}{equations} \Crefname{equation}{Equation}{Equations} \crefname{headlinetheorem}{theorem}{theorems} \Crefname{headlinetheorem}{Theorem}{Theorems} \setlist[enumerate]{itemsep=0.35ex,topsep=0.6ex} \setlist[itemize]{itemsep=0.35ex,topsep=0.6ex}