Change addressing report #1, third comment/typo

Added a sentence to the abstract emphasizing that the available DMFT
data is not sufficient to resolve the open problem in asymptotic
dynamics

2 files changed, 2 insertions, 22 deletions

diff --git a/referee_response.md b/referee_response.md
index 258b489..2dc38cc 100644
--- a/referee_response.md
+++ b/referee_response.md
@@ -1,26 +1,5 @@
 # Report #1
 
-Please find below a short list of comments/ typos:
-
--Some of the results derived for the spherical spin-glass stem from the limit mentioned above. It is clear that this limit may be relevant as some important energy scales are recovered that way. Note however that starting from a regime α=M/N=O(1)
-and taking the limit α→0 should in fact match with the limit M→∞ of the regime M=O(1). Thus there is no guarantee that it should provide relevant information on the case M=1. A direct study of the level set of the spherical spin-glass model as done in Appendix D should allow to confirm this prediction. It was not entirely clear from the manuscript whether this analysis indeed does confirm the relevance of Esh
-
-.
-
--As mentioned by the author, the numerical data does not allow to judge the relevance of the energy scale Esh
-
-and this direction deserves further investigation
-Recommendation
-
-Publish (meets expectations and criteria for this Journal)
-
-    validity: high
-    significance: high
-    originality: high
-    clarity: high
-    formatting: excellent
-    grammar: perfect
-
  * We fixed this typo.
  * The question of limits is a shrewd one, but ultimately the result is the same no matter how the calculation is done. Working directly at *M* = 1, the steps in the appendices are followed up to equation (28). With *M* = 1 and *V*₀² = *N**E*, the second term in the exponential remains of order *N* but the second is of order 1 and becomes another contribution to the prefactor. Comparing the resulting expression with (41) in the limit of α to zero with *V*₀² = *E*²/α, the two approaches result in the same effective action. In fact, an earlier version of this manuscript included two derivations, but the one for *M* of order 1 was deemed redundant in light of this. A note about this point has been added to the amended manuscript.
  * We agree, and further emphasized this in the amended manuscript.
diff --git a/topology.tex b/topology.tex
index 11f1277..99c9a06 100644
--- a/topology.tex
+++ b/topology.tex
@@ -66,7 +66,8 @@ problem and level sets of the energy in the spherical spin glasses. We
 conjecture that the transition energy dividing two of the topological phases
 corresponds to the energy asymptotically reached by gradient descent from a
 random initial condition, possibly resolving an open problem in
-out-of-equilibrium dynamics.
+out-of-equilibrium dynamics. However, the quality of the available data leaves
+the question open.
 }
 }