diff --git a/main.tex b/main.tex
index 1d4bc018e03f8c82385b8846c011551f767ef34c..e456eadc90bc86d369595262e0b9ff098103ba06 100644
--- a/main.tex
+++ b/main.tex
@@ -575,13 +575,19 @@ However, when computing all tilt semistabilizers for $v$ on $\PP^2$, the maximum
 rank that appears turns out to be $\sage{extravagant.actual_rmax}$.
 \end{example}
 
-\section{B.Schmidt's Method}
+\section{B.Schmidt's Wall Finding Method}
 
-Goals:
-\begin{itemize}
-	\item intro
-	\item link repo
-\end{itemize}
+The proof for the previous theorem was hinted at in [ref], but the value appears
+explicitly in [ref]. The latter reference is a SageMath [ref?] library for
+computing certain quantities related to Bridgeland stabilities on Picard rank 1
+varieties. It also includes functions to compute pseudo-walls and
+pseudo-semistabilizers for tilt stability.
+
+Here is an outline of the algorithm involved to do this. Simplifications will be
+made in the presenteation to concentrate on the case we are interested in:
+finding all pseudo-walls when $\beta_{-}\in\QQ$. In section [ref], a different
+algorithm will be presented making use of the later theorems in this article,
+with the goal of cutting down the run time.
 
 \subsection{Strategy}
 
@@ -594,6 +600,38 @@ Goals:
 	\item Stop when conditions fail
 	\item method works same way for both rational beta_{-} but also for walls
 		larger than certain amount
+
+Fix a Chern character $v$ with positive rank, $\Delta(v) \geq 0$,
+and $\beta_{-}(v) \in \QQ$.
+The goal is to find all Chern characters $u=(r,c\ell,d\ell^2)$ which satisfy the
+conditions of lemma \ref{lem:pseudo_wall_numerical_tests} using
+$P=(\beta_{-},0)$, as well as the Bogomolov inequalities:
+$\Delta(u),\Delta(v-u) \geq 0$ and $\Delta(u)+\Delta(v-u) \leq \Delta(v)$.
+We want to restrict our attention to pseudo-walls left of $V_v$ (condition (a) of
+lemma), because this is the side of $V_v$ containing the chamber for Gieseker
+stable objects, and the picture on the other side should be symmetric.
+Condition (c) of the lemma is there to restrict to objects most likely to
+semistabilizers of actual sheaves. The Chern characters which destabilize
+`outwards' can be recovered as $v-u$ for each solution $u$ to the current
+problem.
+
+To do this, first calculate the upper bound $r_{max}$ on the ranks of tilt
+semistabilizers, as given by theorem \ref{thm:loose-bound-on-r}.
+
+Recalling consequence 2 of lemma \ref{lem:pseudo_wall_numerical_tests}, we can
+iterate through the possible values of $\mu(u)=\frac{c}{r}$ taking a decreasing
+sequence of all fractions between $\mu(v)$ and $\beta_{-}$, who's denominators
+are no large than $r_{max}$ (giving a finite sequence). This can be done with Farey sequences [ref], for
+which there exist formulae to generate.
+
+These $\mu(u)$ values determine pairs $r,c$ up to multiples, we can then take
+all multiples which satisy $0<r\geq r_{max}$.
+
+We now have a finite sequence of pairs $r,c$ for which there might be a solution
+to our problem. In particular, any $(r,c\ell,d\ell^2)$ satisfies consequence 2
+of lemma \ref{lem:pseudo_wall_numerical_tests}, and the positive rank condition.
+
+
 \end{itemize}
 
 \subsection{Limitations}