Breaking up 'properties' in the intro into smaller subsections, converting many properties back to theorems, and numbering according to where they occur in the text. Not completely done, e.g. the action map which needs statements made consistent.
\documentclass[11pt,leqno]{amsart}
%\usepackage{amsthm}
\newcommand{\pathtotrunk}{./}
\input{text/article_preamble}
\input{text/top_matter}
\input{text/kw_macros}
%\title{Blob Homology}
\title{Sandbox}
\begin{document}
\begin{equation*}
\mathfig{.4}{tempkw/feb21d}
\end{equation*}
$$
\begin{tikzpicture}[baseline,line width = 2pt]
\draw[blue] (0,0) circle (2);
\fill[red] (0,0) circle (0.1);
\foreach \qm/\qa/\n in {70/-30/0, 120/95/1, -120/180/2} {
\draw[red] (0,0) -- (\qm:2);
\path (\qa:1) node {\color{green!50!brown} $\cA_\n$};
\path (\qm+20:2.5) node(M\n) {\color{green!50!brown} $\cM_\n$};
\draw[line width=1pt, green!50!brown, ->] (M\n.\qm+135) to[out=\qm+135,in=\qm+90] (\qm+5:1.3);
}
\end{tikzpicture}
$$
\end{document}