Add paragraph motivating the main lemma

main.tex

@@ -328,6 +328,16 @@ the circular walls must be nested and non-intersecting.
 
 \subsection{Characteristic curves for pseudo-semistabilizers}
 
+These characteristic curves introduced are convenient tools to think about the
+numerical conditions that can be used to test for pseudo-semistabilizers, and
+for solutions to the problem (\ref{problem:problem-statement-1}).
+In particular, problem (\ref{problem:problem-statement-1}) will be translated to
+a list of numerical inequalities on it's solutions $u$.
+
+The next lemma is a key to making this translation and revolves around the
+geometry and configuration of the characteristic curves involved in a
+semistabilizing sequence.
+
 \begin{lemma}[Numerical tests for left-wall pseudo-semistabilizers]
 \label{lem:pseudo_wall_numerical_tests}
 Let $v$ and $u$ be Chern characters with $\Delta(v),