% Shared preamble for the mathematical companion and its QA supplement.
\usepackage{amsmath,amssymb,amsthm,mathtools,mathrsfs}
\usepackage{booktabs,longtable,array,tabularx}
\usepackage{seqsplit}
\usepackage{enumitem}
\usepackage{needspace}
\usepackage{xcolor}
\usepackage{graphicx}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,calc,positioning}
\usepackage{hyperref}
\usepackage[nameinlink,capitalise,noabbrev]{cleveref}

\hypersetup{
  hidelinks,
  pdfdisplaydoctitle=true
}

\setlist{itemsep=0.35ex,topsep=0.6ex}
\setlength{\emergencystretch}{2em}
\allowdisplaybreaks[2]

\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{claim}[theorem]{Claim}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{construction}[theorem]{Construction}
\newtheorem{convention}[theorem]{Convention}
\theoremstyle{remark}
\newtheorem{remark}[theorem]{Remark}
% ``warning'' remains an internal source alias, but its public surface is the
% conventional Remark environment approved for the compact edition.
\newtheorem{warning}[theorem]{Remark}
% Separate alphabetic counter for introduction-level conceptual statements.
% This does not renumber or alter any theorem in the complete witness chain.
\newtheorem{headlinetheorem}{Theorem}
\renewcommand{\theheadlinetheorem}{\Alph{headlinetheorem}}

\newcommand{\Diff}{\operatorname{Diff}}
\newcommand{\id}{\operatorname{id}}
\newcommand{\Int}{\operatorname{int}}
\newcommand{\Span}{\operatorname{span}}
\newcommand{\im}{\operatorname{im}}
\newcommand{\supp}{\operatorname{supp}}
\newcommand{\mcg}{\operatorname{MCG}}
\newcommand{\Maslov}{\mu}
\newcommand{\Q}{\mathbb Q}
\newcommand{\Z}{\mathbb Z}
\newcommand{\R}{\mathbb R}
\newcommand{\cA}{\mathcal A}
\newcommand{\cB}{\mathcal B}
\newcommand{\cC}{\mathcal C}
\newcommand{\cL}{\mathcal L}
\newcommand{\cN}{\mathcal N}
\newcommand{\cQ}{\mathcal Q}
\newcommand{\cT}{\mathcal T}
\newcommand{\cV}{\mathcal V}
\newcommand{\cW}{\mathcal W}
\newcommand{\Fcut}[1]{\widetilde F_{#1}}
\newcommand{\Fquot}[1]{f_{#1,U}}
\newcommand{\Fglob}[1]{F_{#1}}
\newcommand{\eps}{\varepsilon}
\newcommand{\starv}{\star}
\newcommand{\compose}{\mathbin{\circ}}

\newcommand{\sourcekey}[1]{\texttt{#1}}
\newcommand{\stage}[1]{\textsc{#1}}
\newcommand{\hashtext}[1]{\texttt{\seqsplit{#1}}}

\crefname{construction}{construction}{constructions}
\Crefname{construction}{Construction}{Constructions}
\crefname{convention}{convention}{conventions}
\Crefname{convention}{Convention}{Conventions}
\crefname{headlinetheorem}{theorem}{theorems}
\Crefname{headlinetheorem}{Theorem}{Theorems}
\crefname{warning}{remark}{remarks}
\Crefname{warning}{Remark}{Remarks}