Lots of cleaning up.arxiv.v3

1 files changed, 13 insertions, 10 deletions

diff --git a/response.md b/response.md
index 39042a0..5cbbf0a 100644
--- a/response.md
+++ b/response.md
@@ -98,8 +98,8 @@ specific influence of the covariance function f on the form of RSB has been
 moved into the details for the calculation of the complexity, in subsection
 A.4: Replica ansatz and saddle point. Where it was in section 2 we now say
 
-"The choice of *f* has significant effect on the form of order in the model, and
-this likewise influences the geometry of stationary points."
+"The choice of *f* has significant effect on the form of equilibrium order in
+the model, and likewise influences the geometry of stationary points."
 
 > fig.1, add a caption under each figure saying what they are (oriented
 > saddles, oriented minima, etc), it is much easier to read.
@@ -140,9 +140,10 @@ mode more explicit, as the referee suggests. We do not think it is necessary to
 include a figure for the pure models, instead clarifying the most important
 departure in the text:
 
-"The largest difference is the decoupling of nearby stable points from nearby
-low-energy points: in the pure *p*-spin model, the left and right panels of
-Fig. 3 would be identical up to a constant factor -*p*."
+"The largest difference between the pure and mixed models is the decoupling of
+nearby stable points from nearby low-energy points: in the pure *p*-spin model,
+the left and right panels of Fig. 3 would be identical up to a constant factor
+−*p*."
 
 For those interested in more detailed comparisons, the relevant figure for the
 pure models is found in the paper twice cited in that subsection.
@@ -162,11 +163,13 @@ Fig. 3."
 This sentence has been expanded to make it more clear, and the statement now reads
 
 "Like in the pure models, the minimum energy and maximum stability of nearby
-points are not monotonic: there is a range of overlap where the minimum energy
-of neighbors decreases with proximity. The emergence of oriented index-one
-saddles along the line of lowest-energy states at a given overlap occurs at the
-local minimum of this line, another similarity with the pure models [13]. It is
-not clear why this should be true or what implications it has for behavior."
+points are not monotonic in *q*: there is a range of overlap where the minimum
+energy of neighbors decreases with overlap. The transition from stable minima
+to index-one saddles along the line of lowest-energy states occurs at its local
+minimum, another similarity with the pure models [13]. This point is
+interesting because it describes the properties of the nearest stable minima to
+the reference point. It is not clear why the local minimum of the boundary
+coincides with this point or what implications that has for behavior."
 
 We also now emphasize that the implications are not known. However, the
 coincidence itself it interesting, at the very least for the ability to predict