Fix errors (interlacing environment and scope)

main.tex

@@ -568,6 +568,7 @@ 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_{-}}}
 
@@ -751,7 +752,7 @@ In the other case, $q=\chern^{\beta}_1(F)$, it's the right hand sides of
 (eqn \ref{eqn:positive_rad_d_bound_betamin}) which match.
 
 
-The more generic case, when $0 < q:=\chern_1{\beta}(E) < \chern_1^{\beta}(F)$
+The more generic case, when $0 < q:=\chern_1^{\beta}(E) < \chern_1^{\beta}(F)$
 for the bounds on $d$ in terms of $r$ is illustrated in figure
 (\ref{fig:d_bounds_xmpl_gnrc_q}).
 The question of whether there are pseudo-destabilizers of arbitrarily large
@@ -838,8 +839,8 @@ radius of the pseudo-wall being positive
 	\begin{align*}
 		&\frac{\lcm(m,2n^2)}{2}
 		\max_{q \in [0,\chern_1^\beta(v)]}
-			\\
-			&\left\{
+	\\
+		&\left\{
 			\min
 			\left(
 				q^2,
@@ -850,7 +851,7 @@ radius of the pseudo-wall being positive
 				+q^2
 				+\frac{R}{\lcm(m,2n^2)}
 			\right)
-			\right\}
+		\right\}
 	\end{align*}
 \end{rmax_with_uniform_eps}
 
@@ -940,6 +941,8 @@ and therefore $r$ cannot satisfy this condition for all $q$.
 Taking the maximum of all these expressions over $q$, and substituting the value
 for $\epsilon$ gives the result.
 
+\egroup % end scope where epsilon redefined
+
 \end{proof}
 
 %% refinements using specific values of q and beta
@@ -971,8 +974,6 @@ And so, we also have $\aa(\aa r+2\bb) \equiv \aa\bb$ (mod $2n^2$).
 
 \minorheading{Irrational $\beta$}
 
-\egroup % end scope where epsilon redefined
-
 \egroup % end scope where beta redefined to beta_{-}
 
 \section{Conclusion}