diff --git a/main.tex b/main.tex
index 9bc843685b57fa9fb0b0a6dabe7dfa9548f45f3d..b91585cabaa8b1831008313fade6f08c87779eda 100644
--- a/main.tex
+++ b/main.tex
@@ -277,10 +277,13 @@ $\nu_{\alpha,\beta}(u)=0$, and hence $\chern_2^{\alpha, \beta}(u)=0$. In fact,
 this allows us to use the characteristic curves of some $v$ and $u$ (with
 $\Delta(v), \Delta(u)\geq 0$ and positive ranks) to determine the location of
 the pseudo-wall where $u$ pseudo-semistabilizes $v$. This is done by finding the
-intersection of $\Theta_v$ and $\Theta_u$.
-%TODO ref forwards
+intersection of $\Theta_v$ and $\Theta_u$, the point $(\beta,\alpha)$ where
+$\nu_{\alpha,\beta}(u)=\nu_{\alpha,\beta}(v)=0$, and a pseudo-wall point on
+$\Theta_v$, and hence the apex of the circular pseudo-wall with centre $(\beta,0)$
+(as per subsection \ref{subsect:bertrams-nested-walls}).
 
 \subsection{Bertram's nested wall theorem}
+\label{subsect:bertrams-nested-walls}
 
 Although Bertram's nested wall theorem can be proved more directly, it's also
 important for the content of this document to understand the connection with
@@ -625,10 +628,11 @@ rank that appears turns out to be $\sage{extravagant.actual_rmax}$.
 
 \section{B.Schmidt's Wall Finding Method}
 
-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
+The proof for the previous theorem was hinted at in
+\cite{SchmidtBenjamin2020Bsot}, but the value appears explicitly in
+\cite{SchmidtGithub2020}. The latter reference is a SageMath \cite{sagemath}
+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
@@ -662,8 +666,8 @@ 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.
+are no large than $r_{max}$ (giving a finite sequence). This can be done with
+Farey sequences \cite[chapter 6]{alma994504533502466}, 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 $0<r\leq r_{max}$.
@@ -710,8 +714,8 @@ alternative algorithm which will later be described in this article [ref].
  & $(3, 2\ell, -2)$
  & $(3, 2\ell, -\frac{15}{2})$ \\
  \hline
- Computation time for earlier [ref] program & \sim 20s & >1hr \\
- Computation time for [ref] program  & \sim 50ms & \sim 50ms \\
+ \cite[\texttt{tilt.walls_left}]{SchmidtGithub2020} exec time & \sim 20s & >1hr \\
+ \cite{NaylorRust2023} exec time & \sim 50ms & \sim 50ms \\
  \hline
 \end{tabular}
 \end{center}
@@ -744,8 +748,8 @@ u = Chern_Char(*var("r c d", domain="real"))
 Δ = lambda v: v.Q_tilt()
 \end{sagesilent}
 
-Recall [ref] that $\chern_1^{\beta}$ has fixed bounds in terms of
-$\chern(F)$, and so we can write:
+Recall from eqn \ref{eqn-tilt-cat-cond} that $\chern_1^{\beta}$ has fixed
+bounds in terms of $\chern(F)$, and so we can write:
 
 \begin{sagesilent}
 ts = stability.Tilt
diff --git a/references.bib b/references.bib
index 2b8a8bb15313982afd664b0545578f4379dbf0bf..78f44248d3c9cae41f7e1de6e92b2cc699887378 100644
--- a/references.bib
+++ b/references.bib
@@ -121,4 +121,16 @@
   title = {{S}ageMath, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion 9.6.0)},
   note = {{\tt https://www.sagemath.org}},
   year = {2022}
+}
+@book{alma994504533502466,
+  author = {Niven, Ivan},
+  address = {New York ;},
+  booktitle = {An introduction to the theory of numbers},
+  edition = {Second edition.},
+  keywords = {Number theory},
+  language = {eng},
+  lccn = {66017623},
+  publisher = {Wiley},
+  title = {An introduction to the theory of numbers / Ivan Niven, Herbert S. Zuckerman.},
+  year = {1966},
 }
\ No newline at end of file