Claire's feedback about clarity of parallel dichotomies

main.tex

@@ -24,7 +24,7 @@ Practical Methods for Finding Pseudowalls}
 
 \section{Introduction}
 
-There are theoretical results [ref] that show that for any $\beta_0 \in \QQ$,
+[ref] shows that for any $\beta_0 \in \QQ$,
 the vertical line $\{\sigma_{\alpha,\beta_0} \colon \alpha \in \QQ_{>0}\}$ only
 intersects finitely many walls. A consequence of this is that if
 $\beta_{-} \in \QQ$, then there can only be finitely many circular walls to the