diff --git a/main.tex b/main.tex
index 259a22b91685c40e1879a857c7a894037f1b8d8f..c3f8668e93786dbc80b95169597bee39cc8fc930 100644
--- a/main.tex
+++ b/main.tex
@@ -554,6 +554,12 @@ Suppose we take $\beta = \beta_{-}$ (so that $\chern^{\beta}_2(F)=0$)
 in the previous subsections, to find all circular walls to the left of the
 vertical wall (TODO as discussed in ref).
 
+% redefine \beta (especially coming from rendered SageMath expressions)
+% to be \beta_{-} for the rest of this subsubsection
+\bgroup
+\let\originalbeta\beta
+\renewcommand\beta{{\originalbeta_{-}}}
+
 \begin{align}
 	d &\geq&
 	\sage{bgmlv1_d_lowerbound_linear_term}
@@ -573,7 +579,7 @@ vertical wall (TODO as discussed in ref).
 
 Furthermore, we get an extra bound for $d$ resulting from the condition that the
 radius of the circular wall must be positive. As discussed in (TODO ref), this
-is equivalent to $\chern^{\beta_{-}}_2(E) > 0$, which yields:
+is equivalent to $\chern^{\beta}_2(E) > 0$, which yields:
 
 \begin{sagesilent}
 	positive_radius_condition = (
@@ -589,7 +595,7 @@ is equivalent to $\chern^{\beta_{-}}_2(E) > 0$, which yields:
 \begin{equation*}
 	\sage{positive_radius_condition}
 \end{equation*}
-
+\egroup
 
 \section{Conclusion}