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-\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}