From 0ec2e63a7310d2784b72785346f3cc1a075ff935 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 6 Mar 2023 19:44:33 +0100
Subject: New appeal.

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 appeal.tex | 67 +++++++++++++-------------------------------------------------
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 \begin{document}
 \begin{letter}{
-  Agnese I.~Curatolo, Ph.D.\\
   Physical Review Letters\\
   1 Research Road\\
   Ridge, NY 11961
 }
 
-\opening{Dear Dr.~Curatolo,}
+\opening{To the editors of PRL,}
 
-We wish to appeal the decision concerning our manuscript,
-and expect to take this to the highest level possible in Physical Review.
-Our motivation is scientific, but also one of principle: {\em there should
-not be an implicit bias in favor of partial or purely numerical solutions,
-and against the actual closure of
-a long standing problem, on the basis that the latter is harder to read.}
+We wish to appeal the decision concerning our manuscript \textit{Unveiling the complexity of hierarchical energy landscapes}
+which we submitted to PRL.
 
-Neither of the referees criticize the content of the manuscript. They both
-find the article somewhat technical,
-but it should be born in mind that:
-\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}
+As we mentioned in the reply to the referees, this is a problem that has
+been open for 42 years,
+and several related contributions have been published since in PRL.
 
-The other criticisms are:
+Our solution for the first time gives the full picture of the structure
+of valleys in a complex landscape, finally rendering the ``state counting''
+(Kac-Rice) approach -- used in several hundred papers --
+compatible with the Parisi solution of equilibrium. As a byproduct, the
+structure of near-equilibrium saddles is for the first time transparent.
 
-Referee A remarks that a full connection with dynamics
-is not presented in our paper. This is true, and such a connection does not
-exist at present. We sincerely hope to
-find it, and if we succeed we firmly believe the resulting  article will also be
-worthy of PRL.
-
-Referee B states that
-\begin{enumerate}
-  \item  ``the topic has been studied extensively in  the last thirty years and
-    more'' as a shortcoming, but fails to realize that the solution to the full
-    problem has been open, in spite of all these efforts.
-  \item The meaning of the related remark: ``the only novelty with respect to
-    previous work is that the results are obtained at zero temperature''
-    completely escapes us. Firstly because temperature is not an issue here --
-    it suffices to replace energy by TAP free-energy to introduce it, with
-    essentially no change. Again, the novelty of the article is that generic
-    models, most notably  the Sherrington Kirkpatrick which motivated the first
-    (pioneering but failed) attempt 42 years ago, are now finally accessible.
-  \item ``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.''
-  One could say that development of higher fidelity $q$-bits has failed to
-  deliver the factorization  of large integers up to now, but this is hardly a
-  barrier to publishing substantial progress about their development.
-\end{enumerate}
-
-Again, PRL has devoted a sustained attention to these problems. The referee
-goes on to remark that what is truly important ``involves dynamics and
-activated processes.'' But one of the reasons that they  have not been fully
-understood, as the referee claims correctly, is that these take place
-between states whose geometrical arrangement were not known (except for the
-pure $p$-spin case, or in general, equilibrium), and our work is, we believe, a
-true breakthrough in this direction.
+The reason we are keen to publish in PRL is clear:   PRL gives an
+``official'' sense of closure,
+in a way no other journal does. We believe our article deserves it.
 
 \closing{Sincerely,}
 
-- 
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