From 58cffb6a353f6561b60a9c09837db86549eaeefd Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Mon, 24 Jul 2023 15:39:47 +0100
Subject: [PATCH] Correct references in last 2 commits
---
main.tex | 11 ++++++-----
1 file changed, 6 insertions(+), 5 deletions(-)
diff --git a/main.tex b/main.tex
index 0d40549..e3bf6ab 100644
--- a/main.tex
+++ b/main.tex
@@ -697,6 +697,7 @@ conditions. However, these can be reduced down completely to purely numerical
problem with the help of lemma \ref{lem:pseudo_wall_numerical_tests}.
\begin{lemma}[Numerical Tests for Sufficiently Large `left' Pseudo-walls]
+ \label{lem:num_test_prob1}
Given a Chern character $v$ with positive rank and $\Delta(v) \geq 0$,
and a choice of point $P$ on $\Theta_v^-$.
Solutions $u=(r,c\ell,d\frac{1}{2}\ell^2)$
@@ -726,7 +727,7 @@ problem with the help of lemma \ref{lem:pseudo_wall_numerical_tests}.
\end{proof}
\begin{corrolary}[Numerical Tests for All `left' Pseudo-walls]
-\label{cor:numerical-test-left-pseudowalls-rational-betamin}
+\label{cor:num_test_prob2}
Given a Chern character $v$ with positive rank and $\Delta(v) \geq 0$,
such that $\beta_{-}\coloneqq\beta_{-}(v) \in \QQ$.
Solutions $u=(r,c\ell,d\frac{1}{2}\ell^2)$
@@ -985,8 +986,8 @@ u = Chern_Char(*var("r c d", domain="real"))
\end{sagesilent}
Recall from condition \ref{item:chern1bound:lem:num_test_prob1} in
-lemma \ref{lem:pseudo_wall_numerical_tests}
-(or corrolary \ref{cor:numerical-test-left-pseudowalls-rational-betamin})
+lemma \ref{lem:num_test_prob1}
+(or corrolary \ref{cor:num_test_prob2})
that $\chern_1^{\beta}(u)$ has fixed bounds in terms of $\chern_1^{\beta}(v)$,
and so we can write:
@@ -1019,8 +1020,8 @@ and we shall be varying $\chern_0(E) = r$ to see when certain inequalities fail.
\subsection{Numerical Inequalities}
This section studies the numerical conditions that $u$ must satisfy as per
-lemma \ref{lem:pseudo_wall_numerical_tests}
-(or corrolary \ref{cor:numerical-test-left-pseudowalls-rational-betamin}).
+lemma \ref{lem:num_test_prob1}
+(or corrolary \ref{cor:num_test_prob2})
\subsubsection{Size of pseudo-wall: $\chern_2^P(u)>0$ }
\label{subsect-d-bound-radiuscond}
--
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