From 0208494d7da05396f9dfc1005bb63e3facf37b7a Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Mon, 24 Jul 2023 15:45:57 +0100
Subject: [PATCH] Adjust radius condition investigation to new problem+lemma
 structure

---
 main.tex | 12 ++++++++----
 1 file changed, 8 insertions(+), 4 deletions(-)

diff --git a/main.tex b/main.tex
index e3bf6ab..ba80f41 100644
--- a/main.tex
+++ b/main.tex
@@ -711,6 +711,7 @@ problem with the help of lemma \ref{lem:pseudo_wall_numerical_tests}.
 		\item $0\leq\chern_1^{\beta(P)}(u)\leq\chern_1^{\beta(P)}(v)$
 			\label{item:chern1bound:lem:num_test_prob1}
 		\item $\chern_2^{P}(u)>0$
+			\label{item:radiuscond:lem:num_test_prob1}
 	\end{enumerate}
 \end{lemma}
 
@@ -1026,11 +1027,14 @@ lemma \ref{lem:num_test_prob1}
 \subsubsection{Size of pseudo-wall: $\chern_2^P(u)>0$ }
 \label{subsect-d-bound-radiuscond}
 
-This condition refers to consequence 4 from
-lemma \ref{lem:pseudo_wall_numerical_tests}.
+This condition refers to condition
+\ref{item:radiuscond:lem:num_test_prob1}
+from lemma \ref{lem:num_test_prob1}
+(or corrolary \ref{cor:num_test_prob2}).
 
-In the case where $P$ was chosen to be the base of $\Theta_v^-$: $P=(\beta_{-},0)$.
-This condition amounts to:
+In the case where we are tackling problem \ref{problem:problem-statement-2}
+(with $\beta = \beta_{-}$), this condition, when expressed as a bound on $d$,
+amounts to:
 
 \begin{align}
 \label{eqn:radius-cond-betamin}
-- 
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