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+Because neither referee addressed the scientific content of our paper,
+nor substantively addressed its presentation, we have not submitted a
+revised manuscript. Below, we respond to the referees' comments.
+
+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 says 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.
+
+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, but believe that the technique for
+computing the quenched complexity is a major breakthrough. Just
+because this new technique is demonstrated on the simplest toy models
+should not discount its importance and potential.
+
+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. 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
+> 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.
+>
+> I recommend that the paper is not published in PRL while the companion
+> paper is worth publishing on PRE.
+
+We disagree with the statement of Referee B that "the only novelty
+with respect to previous work is that the results are obtained at zero
+temperature". 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 "[e]ssential open problems in
+the field," and agree that our work does not deliver answers. However,
+delivering answers for 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.