\usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsfonts,amssymb,mathtools,amsthm} \usepackage{graphicx} \usepackage{enumitem} \usepackage{orcidlink} \usepackage{xurl} \usepackage{booktabs} \usepackage{placeins} \usepackage{slashed} \usepackage{tikz} \usetikzlibrary{arrows.meta,calc,positioning,decorations.markings} \newcommand{\bC}{\mathbb{C}} \newcommand{\bR}{\mathbb{R}} \newcommand{\bZ}{\mathbb{Z}} \newcommand{\nsl}{\slashed{n}} \newcommand{\msl}{\slashed{m}} \newcommand{\usl}{\slashed{u}} \newcommand{\Pup}{P^{\uparrow}} \newcommand{\Pdn}{P^{\downarrow}} \newcommand{\Khat}{\widehat{K}} \newcommand{\Sym}{\operatorname{Sym}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\Spin}{\operatorname{Spin}} \newcommand{\Cl}{\operatorname{Cl}} \newcommand{\tr}{\operatorname{tr}} \newcommand{\Span}{\operatorname{span}} \newcommand{\ad}{\mathfrak{g}} \newcommand{\doilink}[1]{\href{https://doi.org/#1}{\nolinkurl{doi:#1}}} \newcommand{\arxiv}[1]{\href{https://arxiv.org/abs/#1}{\nolinkurl{arXiv:#1}}} \theoremstyle{plain} \newtheorem{theorem}{Theorem}[section] \newtheorem{proposition}[theorem]{Proposition} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{corollary}[theorem]{Corollary} \newtheorem*{maintheorem}{Main Theorem} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{remark}[theorem]{Remark} \newtheorem{example}[theorem]{Example} \raggedbottom \hbadness=5000 \emergencystretch=3em