From 145d4716478344e6ec7748c5df814e85dee56a43 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Tue, 9 Mar 2021 15:58:49 +0100
Subject: Working tweak.s

---
 bezout.tex | 19 ++++++++++---------
 1 file changed, 10 insertions(+), 9 deletions(-)

(limited to 'bezout.tex')

diff --git a/bezout.tex b/bezout.tex
index 1b9f04e..ff5a840 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -102,15 +102,16 @@ One might balk at taking the constraint as $z^2=N$---which might be more
 appropriately called a hyperbolic constraint---rather than $|z|^2=N$.  The
 reasoning is twofold. First, at every point $z$ the energy
 \eqref{eq:bare.hamiltonian} has a `radial' gradient of magnitude proportional
-to itself, as $z\cdot\partial H_0=pH_0$. This trivial direction must be removed
-if critical points are to exist a any nonzero energy, and the constraint
-surface $z^2=N$ is the unique surface whose normal is parallel to $z$ and which
-contains the real configuration space as a subspace. Second, taking the
-constraint to be the level set of a holomorphic function means the resulting
-configuration space is a \emph{bone fide} complex manifold, and therefore
-admits easy generalization of the integration techniques referenced above. The
-same cannot be said for the space defined by $|z|^2=N$, which is topologically
-the $(2N-1)$-sphere and cannot admit a complex structure.
+to the energy, as $z\cdot\partial H_0=pH_0$. This trivial direction must be
+removed if critical points are to exist a any nonzero energy, and the
+constraint surface $z^2=N$ is the unique surface whose normal is parallel to
+$z$ and which contains the configuration space of the real $p$-spin model as a
+subspace. Second, taking the constraint to be the level set of a holomorphic
+function means the resulting configuration space is a \emph{bone fide} complex
+manifold, and therefore permits easy generalization of the integration
+techniques referenced above. The same cannot be said for the space defined by
+$|z|^2=N$, which is topologically the $(2N-1)$-sphere and cannot admit a
+complex structure.
 
 The critical points are of $H$ given by the solutions to the set of equations
 \begin{equation} \label{eq:polynomial}
-- 
cgit v1.2.3-54-g00ecf

