\usepackage{amsmath,amssymb,amsthm,mathtools,mathrsfs} \usepackage{booktabs} \usepackage{enumitem} \usepackage{tikz} \usetikzlibrary{arrows.meta,calc,positioning} \usepackage[hidelinks]{hyperref} \usepackage[nameinlink,noabbrev]{cleveref} \hypersetup{ pdfauthor={Haoyu Sun}, pdftitle={Fixed-Level TQFT Transport of Marked Handleslide Coherence: Disjoint Cubes and a Three-Handle Pentagon}, pdfsubject={Fixed-level TQFT transport of marked handleslide coherence, disjoint cubes, and a three-handle pentagon}, pdfkeywords={FixedLevelQuantumHandleslideCoherence2026} } \newtheorem{theorem}{Theorem}[section] % Independent alphabetic counter for citable introduction-level restatements. % The numbered formal theorem chain below is intentionally unchanged. \newtheorem{headlinetheorem}{Theorem} \renewcommand{\theheadlinetheorem}{\Alph{headlinetheorem}} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{corollary}[theorem]{Corollary} % Keep the source alias while using a conventional reader-visible class. \newtheorem{inputtheorem}[theorem]{Theorem} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{standinginput}[theorem]{Standing input} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \crefname{headlinetheorem}{theorem}{theorems} \Crefname{headlinetheorem}{Theorem}{Theorems} \crefname{inputtheorem}{theorem}{theorems} \Crefname{inputtheorem}{Theorem}{Theorems} \newcommand{\EK}{E_K} \newcommand{\FK}{F_K} \newcommand{\MKd}{\mathcal M_{K,d}} \newcommand{\VKd}{\mathcal V^+_{K,d}} \newcommand{\MQd}[1]{\mathcal M_{K,d}^{#1}} \newcommand{\Qcore}[1]{Q_{K,d}^{#1}} \newcommand{\Tcore}[2]{\mathsf T_{#1}^{K,#2}} \newcommand{\COMPQ}{\mathrm{COMP}\text{-}Q}