From c4182fa022ceebd61cfbfe258fbc0f3294ea72cb Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 23 Jan 2023 11:56:07 +0100
Subject: Changed file format of response letter.

---
 response.tex | 209 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 209 insertions(+)
 create mode 100644 response.tex

(limited to 'response.tex')

diff --git a/response.tex b/response.tex
new file mode 100644
index 0000000..1709e15
--- /dev/null
+++ b/response.tex
@@ -0,0 +1,209 @@
+\documentclass[a4paper]{letter}
+
+\usepackage[utf8]{inputenc} % why not type "Bézout" with unicode?
+\usepackage[T1]{fontenc} % vector fonts plz
+\usepackage{newtxtext,newtxmath} % Times for PR
+\usepackage[
+  colorlinks=true,
+  urlcolor=purple,
+  linkcolor=black,
+  citecolor=black,
+  filecolor=black,
+]{hyperref} % ref and cite links with pretty colors
+\usepackage{xcolor}
+\usepackage[style=phys]{biblatex}
+
+\renewcommand{\thefootnote}{\fnsymbol{footnote}}
+
+\addbibresource{frsb_kac-rice.bib}
+
+\signature{
+  \vspace{-6\medskipamount}
+  \smallskip
+  Jaron Kent-Dobias \& Jorge Kurchan
+}
+
+\address{
+  Laboratoire de Physique\\
+  Ecole Normale Sup\'erieure\\
+  24 rue Lhomond\\ 
+  75005 Paris
+}
+
+\begin{document}
+\begin{letter}{
+  Agnese I.~Curatolo, Ph.D.\\
+  Physical Review Letters\\
+  1 Research Road\\
+  Ridge, NY 11961
+}
+
+\opening{Dear Dr.~Curatolo,}
+
+Enclosed please find a revised manuscript.
+Neither referee  criticized  the scientific content of our paper,
+nor substantively addressed its presentation. We have followed their comments
+in the direction of  highlighting the importance of having a full solution. In particular
+we have emphasized that going to the full replica treatment uncovers a phase-space structure that needs to be taken into account, and that is absent in the annealed treatment.
+
+
+We have thus added the paragraph:
+
+{\color{red} 
+Having  a full, exact  (`quenched') solution of the generic problem  is not 
+primarily a matter of {\em accuracy}.
+Very basic structural questions are omitted in the approximate `annealed' solution. What is lost  is  the nature, at any given
+energy (or free energy) level, of the stationary points in a generic energy function: at low energies are they basically all minima, with  an exponentially small number of saddles, or
+-- as we show here -- do they consist of a mixture of saddles whose index -- the number of unstable directions -- is a smoothly distributed number? 
+These questions need to be answered for the understanding of the relevance of more complex objects such as
+barrier crossing (which barriers?) \cite{Ros_2019_Complexity, Ros_2021_Dynamical}, or the fate of long-time dynamics
+(which end in what kind of  target states?). 
+
+}
+
+Both referees find that our paper is clearly written but technical, and
+that its topic of "the different RSB schemes" are not suitable for a
+broad audience. This is surprising to the authors, since a quick
+search on Google Scholar reveals several recent PRLs with heavy use of
+RSB schemes. 
+
+We would also like to submit to the referees  that it is somewhat
+incongruous that the solution to a problem that had remained open for 42 years -- during which it was always present in articles in PRL and PRX -- is rejected
+because  it demands of the readers a slightly longer attention span. 
+
+
+
+
+\begin{enumerate}
+  \item PRL has been publishing articles on precisely this problem in the
+    last 30 years.\footfullcite{Fyodorov_2004_Complexity, Bray_2007_Statistics, Fyodorov_2012_Critical, Wainrib_2013_Topological}
+  \item These works were often limited by the fact that general landscapes (for
+    which an annealed solution is not exact) were inaccessible. It is perhaps
+    true that the final solution of an open problem may often be more technical
+    than the previous ones.
+\end{enumerate}
+
+
+
+Below, we respond to the referees' comments.
+
+{\it Report of Referee A -- LY17256/Kent-Dobias
+ The authors consider spin glass models with mixed p-spin interactions
+ on the N-Sphere and calculate the number of stationary points, the
+ logarithm of which yields the complexity. The disorder average of this
+ logarithm is computed with the replica trick, and for different model
+ variants different replica symmetry breaking (RSB) solutions are
+ obtained. A new feature of the solutions, in contrast to previous
+ replica symmetric calculations, is that RSB must occur in parts of the
+ energy-stability phase diagram.
+
+ The paper is clearly written although the content is rather technical
+ and probably only accessible to experts in mean field spin glass
+ models and the different RSB schemes developed in this field. In
+ connection with the well-studied p=3 spin glass model it is briefly
+ mentioned that the complexity and its transitions as a function of
+ energy and/or stability is relevant for the equilibrium and the
+ dynamical behavior of this model – but such a connection has not been
+ made here.
+
+ Therefore, I feel that the results presented here are only interesting
+ for group of experts and I do not assess the finding that the
+ complexity of mixed p-spin glass models shows RSB as a major
+ breakthrough in the field. Therefore, the manuscript is not suitable
+ for publication in Phys. Rev. Lett., and the publication of the
+ accompanying longer paper, submitted to PRE, is sufficient to
+ disseminate the results summarized in this manuscript.}
+
+
+
+Referee A correctly points out that one new feature of the solutions
+outlined in our manuscript is that RSB must occur in parts of the
+phase diagram for these models. However, they neglect another feature:
+that they are the solutions of the *quenched* complexity, which has
+not been correctly calculated until now. We agree with the referee
+that "the complexity of the mixed p-spin glass models" is not a major
+breakthrough in and of itself, we just
+chose to demonstrate  the problem in simplest toy model. But believe that the technique for
+computing the quenched complexity is a major breakthrough  
+{\bf because it brings in the features of organization of saddles of all
+kinds that are invisible in the annealed scheme}. 
+
+
+Referee A states that a connection between the complexity and the
+equilibrium and dynamical behavior is not made in our paper. Until
+recently, this connection was taken for granted, and the demonstration
+that the standard correspondence does not hold in the mixed p-spin
+spherical models was exciting enough news to be published in PRX 10,
+031045 (2020). It is true that our work doesn't solve the problem that
+paper opened, but it does deepen it by showing definitively that the
+use of RSB and the quenched complexity are not sufficient to
+reestablish a landscape–dynamics connection. 
+{\bf One can hardly expect that the structure of saddles at a given energy may be connected
+with dynamics (for example in Sherrington Kirkpatrick) if it is unknown}.
+%We disagree with the
+%referee's implicit assertion that only clean resolutions, and not the
+%compelling deepening of problems, are worthy of a broad audience.
+
+Report of Referee B -- LY17256/Kent-Dobias
+{\it  The paper presents a computation of the complexity in spherical
+ spin-glass models. Neither the techniques nor the results are
+ sufficiently new and relevant to justify publication on PRL. This is
+ not surprising given that the topic has been studied extensively in
+ the last thirty years and more, the only novelty with respect to
+ previous work is that the results are obtained at zero temperature but
+ this is definitively not enough. Essential open problems in the field
+ involves dynamics and activated processes and some results have
+ appeared recently, instead the analysis of the static landscape, to
+ which the present paper is a variation, failed to deliver answers to
+ these questions up to now.
+
+ }
+
+Concerning the statement of Referee B that "the only novelty
+with respect to previous work is that the results are obtained at zero
+temperature", we do not know what to make of the referee's statement.
+The novelty of the paper is most definitely
+not the fact of treating a zero temperature case. 
+We have added the following phrase, that should clarify the situation:
+
+{\color{blue}
+  For simplicity we have concentrated here on the energy, rather
+than  {\em free-energy} landscape, although the latter is sometimes
+more appropriate. From the technical point of view, this makes no fundamental difference, it suffices 
+to apply the same computation to the Thouless-Andreson-Palmer \cite{Crisanti_1995_Thouless-Anderson-Palmer} (TAP) free energy, instead of the energy. We do not expect new features or technical 
+complications arise.
+
+}
+
+
+%For a system where the quenched and annealed
+%complexities differ, there has not been a correct calculation of the
+%quenched complexity at finite temperature. (and, besides our work,
+%only once or twice at zero temperature, e.g., PRX 9, 011003 (2019).)
+%Rejecting a paper based on a severe misconception of its contents or
+%of the state of the field is not appropriate.
+
+We agree with Referee B's assessment of "essential open problems in
+the field," and agree that our work does not deliver answers. However,
+delivering answers for all essential open problems is not the acceptance
+criterion of PRL. These are
+
+  - Open a new research area, or a new avenue within an established area.
+  - Solve, or make essential steps towards solving, a critical problem.
+  - Introduce techniques or methods with significant impact.
+  - Be of unusual intrinsic interest to PRL's broad audience.
+
+We believe our manuscript makes essential steps toward solving the
+critical problem of connecting analysis of the static landscape to
+dynamics. We believe that its essential step is through the
+introduction of a new technique, calculation of the quenched
+complexity, which we believe will have significant impact as it is
+applied to more complicated models.
+
+\closing{Sincerely,}
+
+\vspace{1em}
+
+\end{letter}
+
+\end{document}
-- 
cgit v1.2.3-70-g09d2


From 4045e729291d6a589fd48c79a154be9f81a1f2ad Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 23 Jan 2023 12:00:35 +0100
Subject: Fancier formatting.

---
 response.tex | 93 ++++++++++++++++++++++++++++++++----------------------------
 1 file changed, 49 insertions(+), 44 deletions(-)

(limited to 'response.tex')

diff --git a/response.tex b/response.tex
index 1709e15..4917d67 100644
--- a/response.tex
+++ b/response.tex
@@ -87,33 +87,35 @@ because  it demands of the readers a slightly longer attention span.
 
 Below, we respond to the referees' comments.
 
-{\it Report of Referee A -- LY17256/Kent-Dobias
- The authors consider spin glass models with mixed p-spin interactions
- on the N-Sphere and calculate the number of stationary points, the
- logarithm of which yields the complexity. The disorder average of this
- logarithm is computed with the replica trick, and for different model
- variants different replica symmetry breaking (RSB) solutions are
- obtained. A new feature of the solutions, in contrast to previous
- replica symmetric calculations, is that RSB must occur in parts of the
- energy-stability phase diagram.
-
- The paper is clearly written although the content is rather technical
- and probably only accessible to experts in mean field spin glass
- models and the different RSB schemes developed in this field. In
- connection with the well-studied p=3 spin glass model it is briefly
- mentioned that the complexity and its transitions as a function of
- energy and/or stability is relevant for the equilibrium and the
- dynamical behavior of this model – but such a connection has not been
- made here.
-
- Therefore, I feel that the results presented here are only interesting
- for group of experts and I do not assess the finding that the
- complexity of mixed p-spin glass models shows RSB as a major
- breakthrough in the field. Therefore, the manuscript is not suitable
- for publication in Phys. Rev. Lett., and the publication of the
- accompanying longer paper, submitted to PRE, is sufficient to
- disseminate the results summarized in this manuscript.}
-
+Report of Referee A -- LY17256/Kent-Dobias
+\begin{quote}
+  \it
+     The authors consider spin glass models with mixed p-spin interactions
+     on the N-Sphere and calculate the number of stationary points, the
+     logarithm of which yields the complexity. The disorder average of this
+     logarithm is computed with the replica trick, and for different model
+     variants different replica symmetry breaking (RSB) solutions are
+     obtained. A new feature of the solutions, in contrast to previous
+     replica symmetric calculations, is that RSB must occur in parts of the
+     energy-stability phase diagram.
+
+     \hspace{2em}The paper is clearly written although the content is rather technical
+     and probably only accessible to experts in mean field spin glass
+     models and the different RSB schemes developed in this field. In
+     connection with the well-studied p=3 spin glass model it is briefly
+     mentioned that the complexity and its transitions as a function of
+     energy and/or stability is relevant for the equilibrium and the
+     dynamical behavior of this model – but such a connection has not been
+     made here.
+
+     \hspace{2em}Therefore, I feel that the results presented here are only interesting
+     for group of experts and I do not assess the finding that the
+     complexity of mixed p-spin glass models shows RSB as a major
+     breakthrough in the field. Therefore, the manuscript is not suitable
+     for publication in Phys. Rev. Lett., and the publication of the
+     accompanying longer paper, submitted to PRE, is sufficient to
+     disseminate the results summarized in this manuscript.
+\end{quote}
 
 
 Referee A correctly points out that one new feature of the solutions
@@ -145,19 +147,20 @@ with dynamics (for example in Sherrington Kirkpatrick) if it is unknown}.
 %compelling deepening of problems, are worthy of a broad audience.
 
 Report of Referee B -- LY17256/Kent-Dobias
-{\it  The paper presents a computation of the complexity in spherical
- spin-glass models. Neither the techniques nor the results are
- sufficiently new and relevant to justify publication on PRL. This is
- not surprising given that the topic has been studied extensively in
- the last thirty years and more, the only novelty with respect to
- previous work is that the results are obtained at zero temperature but
- this is definitively not enough. Essential open problems in the field
- involves dynamics and activated processes and some results have
- appeared recently, instead the analysis of the static landscape, to
- which the present paper is a variation, failed to deliver answers to
- these questions up to now.
-
- }
+\begin{quote}
+  \textit{The paper presents a computation of the complexity in spherical
+     spin-glass models. Neither the techniques nor the results are
+     sufficiently new and relevant to justify publication on PRL. This is
+     not surprising given that the topic has been studied extensively in
+     the last thirty years and more, the only novelty with respect to
+     previous work is that the results are obtained at zero temperature but
+     this is definitively not enough. Essential open problems in the field
+     involves dynamics and activated processes and some results have
+     appeared recently, instead the analysis of the static landscape, to
+     which the present paper is a variation, failed to deliver answers to
+     these questions up to now.
+   }
+\end{quote}
 
 Concerning the statement of Referee B that "the only novelty
 with respect to previous work is that the results are obtained at zero
@@ -188,10 +191,12 @@ the field," and agree that our work does not deliver answers. However,
 delivering answers for all essential open problems is not the acceptance
 criterion of PRL. These are
 
-  - Open a new research area, or a new avenue within an established area.
-  - Solve, or make essential steps towards solving, a critical problem.
-  - Introduce techniques or methods with significant impact.
-  - Be of unusual intrinsic interest to PRL's broad audience.
+\begin{itemize}
+  \item Open a new research area, or a new avenue within an established area.
+  \item Solve, or make essential steps towards solving, a critical problem.
+  \item Introduce techniques or methods with significant impact.
+  \item Be of unusual intrinsic interest to PRL's broad audience.
+\end{itemize}
 
 We believe our manuscript makes essential steps toward solving the
 critical problem of connecting analysis of the static landscape to
-- 
cgit v1.2.3-70-g09d2


From df2fbf0ee2627c67b0212ac6d549a042038abbe7 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 23 Jan 2023 12:09:24 +0100
Subject: Some formatting changes and new references.

---
 response.tex | 9 ++++-----
 1 file changed, 4 insertions(+), 5 deletions(-)

(limited to 'response.tex')

diff --git a/response.tex b/response.tex
index 4917d67..3454eaf 100644
--- a/response.tex
+++ b/response.tex
@@ -49,17 +49,16 @@ we have emphasized that going to the full replica treatment uncovers a phase-spa
 
 We have thus added the paragraph:
 
-{\color{red} 
+\begin{quote}
 Having  a full, exact  (`quenched') solution of the generic problem  is not 
 primarily a matter of {\em accuracy}.
 Very basic structural questions are omitted in the approximate `annealed' solution. What is lost  is  the nature, at any given
 energy (or free energy) level, of the stationary points in a generic energy function: at low energies are they basically all minima, with  an exponentially small number of saddles, or
 -- as we show here -- do they consist of a mixture of saddles whose index -- the number of unstable directions -- is a smoothly distributed number? 
 These questions need to be answered for the understanding of the relevance of more complex objects such as
-barrier crossing (which barriers?) \cite{Ros_2019_Complexity, Ros_2021_Dynamical}, or the fate of long-time dynamics
+barrier crossing (which barriers?) \footfullcite{Ros_2019_Complexity, Ros_2021_Dynamical}, or the fate of long-time dynamics
 (which end in what kind of  target states?). 
-
-}
+\end{quote}
 
 Both referees find that our paper is clearly written but technical, and
 that its topic of "the different RSB schemes" are not suitable for a
@@ -76,7 +75,7 @@ because  it demands of the readers a slightly longer attention span.
 
 \begin{enumerate}
   \item PRL has been publishing articles on precisely this problem in the
-    last 30 years.\footfullcite{Fyodorov_2004_Complexity, Bray_2007_Statistics, Fyodorov_2012_Critical, Wainrib_2013_Topological}
+    last 30 years.\footfullcite{Fyodorov_2004_Complexity, Bray_2007_Statistics, Fyodorov_2012_Critical, Wainrib_2013_Topological, Dennis_2020_Jamming}
   \item These works were often limited by the fact that general landscapes (for
     which an annealed solution is not exact) were inaccessible. It is perhaps
     true that the final solution of an open problem may often be more technical
-- 
cgit v1.2.3-70-g09d2


From 255cd496d8ba4a115ba670a64c8445a8b9c2f485 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 23 Jan 2023 12:34:04 +0100
Subject: More small changes.

---
 frsb_kac-rice.bib | 2 +-
 response.tex      | 7 ++-----
 2 files changed, 3 insertions(+), 6 deletions(-)

(limited to 'response.tex')

diff --git a/frsb_kac-rice.bib b/frsb_kac-rice.bib
index 37ffb2d..6a2b5e8 100644
--- a/frsb_kac-rice.bib
+++ b/frsb_kac-rice.bib
@@ -294,7 +294,7 @@
 
 @article{Crisanti_1995_Thouless-Anderson-Palmer,
  author = {Crisanti, A. and Sommers, H.-J.},
- title = {Thouless-Anderson-Palmer Approach to the Spherical $p$-Spin Spin Glass Model},
+ title = {{Thouless}-{Anderson}-{Palmer} Approach to the Spherical $p$-Spin Spin Glass Model},
  journal = {Journal de Physique I},
  publisher = {EDP Sciences},
  year = {1995},
diff --git a/response.tex b/response.tex
index 3454eaf..6abde6c 100644
--- a/response.tex
+++ b/response.tex
@@ -126,7 +126,7 @@ that "the complexity of the mixed p-spin glass models" is not a major
 breakthrough in and of itself, we just
 chose to demonstrate  the problem in simplest toy model. But believe that the technique for
 computing the quenched complexity is a major breakthrough  
-{\bf because it brings in the features of organization of saddles of all
+\textit{because it brings in the features of organization of saddles of all
 kinds that are invisible in the annealed scheme}. 
 
 
@@ -168,15 +168,12 @@ The novelty of the paper is most definitely
 not the fact of treating a zero temperature case. 
 We have added the following phrase, that should clarify the situation:
 
-{\color{blue}
   For simplicity we have concentrated here on the energy, rather
 than  {\em free-energy} landscape, although the latter is sometimes
 more appropriate. From the technical point of view, this makes no fundamental difference, it suffices 
-to apply the same computation to the Thouless-Andreson-Palmer \cite{Crisanti_1995_Thouless-Anderson-Palmer} (TAP) free energy, instead of the energy. We do not expect new features or technical 
+to apply the same computation to the Thouless-Andreson-Palmer  (TAP) free energy, \footfullcite{Crisanti_1995_Thouless-Anderson-Palmer} instead of the energy. We do not expect new features or technical 
 complications arise.
 
-}
-
 
 %For a system where the quenched and annealed
 %complexities differ, there has not been a correct calculation of the
-- 
cgit v1.2.3-70-g09d2


From 2f2cda1c805ef73408b5a9e3bc3dcab1b8fffe7d Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 23 Jan 2023 14:22:31 +0100
Subject: Removed some comments and changed some formatting.

---
 response.tex | 19 ++++++-------------
 1 file changed, 6 insertions(+), 13 deletions(-)

(limited to 'response.tex')

diff --git a/response.tex b/response.tex
index 6abde6c..13c220f 100644
--- a/response.tex
+++ b/response.tex
@@ -86,8 +86,10 @@ because  it demands of the readers a slightly longer attention span.
 
 Below, we respond to the referees' comments.
 
-Report of Referee A -- LY17256/Kent-Dobias
 \begin{quote}
+  \begin{center}
+    Report of Referee A -- LY17256/Kent-Dobias
+  \end{center}
   \it
      The authors consider spin glass models with mixed p-spin interactions
      on the N-Sphere and calculate the number of stationary points, the
@@ -141,12 +143,11 @@ use of RSB and the quenched complexity are not sufficient to
 reestablish a landscape–dynamics connection. 
 {\bf One can hardly expect that the structure of saddles at a given energy may be connected
 with dynamics (for example in Sherrington Kirkpatrick) if it is unknown}.
-%We disagree with the
-%referee's implicit assertion that only clean resolutions, and not the
-%compelling deepening of problems, are worthy of a broad audience.
 
-Report of Referee B -- LY17256/Kent-Dobias
 \begin{quote}
+  \begin{center}
+    Report of Referee B -- LY17256/Kent-Dobias
+  \end{center}
   \textit{The paper presents a computation of the complexity in spherical
      spin-glass models. Neither the techniques nor the results are
      sufficiently new and relevant to justify publication on PRL. This is
@@ -174,14 +175,6 @@ more appropriate. From the technical point of view, this makes no fundamental di
 to apply the same computation to the Thouless-Andreson-Palmer  (TAP) free energy, \footfullcite{Crisanti_1995_Thouless-Anderson-Palmer} instead of the energy. We do not expect new features or technical 
 complications arise.
 
-
-%For a system where the quenched and annealed
-%complexities differ, there has not been a correct calculation of the
-%quenched complexity at finite temperature. (and, besides our work,
-%only once or twice at zero temperature, e.g., PRX 9, 011003 (2019).)
-%Rejecting a paper based on a severe misconception of its contents or
-%of the state of the field is not appropriate.
-
 We agree with Referee B's assessment of "essential open problems in
 the field," and agree that our work does not deliver answers. However,
 delivering answers for all essential open problems is not the acceptance
-- 
cgit v1.2.3-70-g09d2


From 463f9092809df7e2f76479ee2217078bdaee2692 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 23 Jan 2023 14:31:45 +0100
Subject: Some condesing of the language.

---
 response.tex | 42 ++++++++++++++++++------------------------
 1 file changed, 18 insertions(+), 24 deletions(-)

(limited to 'response.tex')

diff --git a/response.tex b/response.tex
index 13c220f..4addddf 100644
--- a/response.tex
+++ b/response.tex
@@ -61,27 +61,21 @@ barrier crossing (which barriers?) \footfullcite{Ros_2019_Complexity, Ros_2021_D
 \end{quote}
 
 Both referees find that our paper is clearly written but technical, and
-that its topic of "the different RSB schemes" are not suitable for a
+that its topic of ``the different RSB schemes'' are not suitable for a
 broad audience. This is surprising to the authors, since a quick
 search on Google Scholar reveals several recent PRLs with heavy use of
 RSB schemes. 
 
-We would also like to submit to the referees  that it is somewhat
-incongruous that the solution to a problem that had remained open for 42 years -- during which it was always present in articles in PRL and PRX -- is rejected
-because  it demands of the readers a slightly longer attention span. 
-
-
-
-
-\begin{enumerate}
-  \item PRL has been publishing articles on precisely this problem in the
-    last 30 years.\footfullcite{Fyodorov_2004_Complexity, Bray_2007_Statistics, Fyodorov_2012_Critical, Wainrib_2013_Topological, Dennis_2020_Jamming}
-  \item These works were often limited by the fact that general landscapes (for
-    which an annealed solution is not exact) were inaccessible. It is perhaps
-    true that the final solution of an open problem may often be more technical
-    than the previous ones.
-\end{enumerate}
-
+We would also like to submit to the referees  that it is somewhat incongruous
+that the solution to a problem that had remained open for 42 years -- during
+which it was always present in articles in PRL
+\footfullcite{Fyodorov_2004_Complexity, Bray_2007_Statistics,
+Fyodorov_2012_Critical, Wainrib_2013_Topological, Dennis_2020_Jamming}-- is
+rejected because  it demands of the readers a slightly longer attention span.
+These previous works were often limited by the fact that general landscapes
+(for which an annealed solution is not exact) were inaccessible. It is perhaps
+true that the final solution of an open problem may often be more technical
+than the previous ones.
 
 
 Below, we respond to the referees' comments.
@@ -113,7 +107,7 @@ Below, we respond to the referees' comments.
      for group of experts and I do not assess the finding that the
      complexity of mixed p-spin glass models shows RSB as a major
      breakthrough in the field. Therefore, the manuscript is not suitable
-     for publication in Phys. Rev. Lett., and the publication of the
+     for publication in Phys.\ Rev.\ Lett., and the publication of the
      accompanying longer paper, submitted to PRE, is sufficient to
      disseminate the results summarized in this manuscript.
 \end{quote}
@@ -122,9 +116,9 @@ Below, we respond to the referees' comments.
 Referee A correctly points out that one new feature of the solutions
 outlined in our manuscript is that RSB must occur in parts of the
 phase diagram for these models. However, they neglect another feature:
-that they are the solutions of the *quenched* complexity, which has
+that they are the solutions of the \textit{quenched} complexity, which has
 not been correctly calculated until now. We agree with the referee
-that "the complexity of the mixed p-spin glass models" is not a major
+that ``the complexity of the mixed p-spin glass models'' is not a major
 breakthrough in and of itself, we just
 chose to demonstrate  the problem in simplest toy model. But believe that the technique for
 computing the quenched complexity is a major breakthrough  
@@ -162,9 +156,9 @@ with dynamics (for example in Sherrington Kirkpatrick) if it is unknown}.
    }
 \end{quote}
 
-Concerning the statement of Referee B that "the only novelty
+Concerning the statement of Referee B that ``the only novelty
 with respect to previous work is that the results are obtained at zero
-temperature", we do not know what to make of the referee's statement.
+temperature,'' we do not know what to make of the referee's statement.
 The novelty of the paper is most definitely
 not the fact of treating a zero temperature case. 
 We have added the following phrase, that should clarify the situation:
@@ -175,8 +169,8 @@ more appropriate. From the technical point of view, this makes no fundamental di
 to apply the same computation to the Thouless-Andreson-Palmer  (TAP) free energy, \footfullcite{Crisanti_1995_Thouless-Anderson-Palmer} instead of the energy. We do not expect new features or technical 
 complications arise.
 
-We agree with Referee B's assessment of "essential open problems in
-the field," and agree that our work does not deliver answers. However,
+We agree with Referee B's assessment of ``essential open problems in
+the field,'' and agree that our work does not deliver answers. However,
 delivering answers for all essential open problems is not the acceptance
 criterion of PRL. These are
 
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