Changed one response.

1 files changed, 1 insertions, 2 deletions

diff --git a/referee_response.md b/referee_response.md
index a86b265..fd06c71 100644
--- a/referee_response.md
+++ b/referee_response.md
@@ -30,7 +30,6 @@
    * In this manuscript we present what we consider to be the simplest interpretation of the calculation, but the referee is correct to point out that a large Euler characteristic could indicate a complicated product manifold as well as one with many connected components, or other exotic manifolds besides. Our intuition for this is that applying one constraint amounts to taking a smooth, non-self-intersecting slice of a sphere, which should typically produce spheres of one fewer dimension. Repeating this reasoning recursively leads to the conclusion that the result is mostly unions of spheres all the way down. This schematic argument has been added to the manuscript as a footnote in section 2.3. As to what dynamics might look like in a problem where the manifold of solutions were actually a nontrivial product manifold, we have no idea.
  4. The referee points out that previous work on gradient descent in the spherical spin glasses studied gradient descent from both uniformly random initial conditions ("infinite" temperature) and initial conditions drawn from a Boltzmann distribution at some finite temperature, and found that the final state of the dynamics reached marginal minima in a range of energies depending on the initial condition. The conjecture in this manuscript seeks only to explain the upper energy of this range, that associated with gradient descent from a uniformly random initial condition. Presumably there are a variety of behaviors observable by choosing initial conditions using a variety of initial distributions, Boltzmann or otherwise, and one day we may hope to address such questions using similar approaches to this paper. However, this is not addressed here. A small discussion of this point has been added to the manuscript.
    * A paragraph addressing what might occur in planted models has been added to the manuscript.
- 5. Make a supplementary materials file
-   * The manuscript has been modified to clarify where a review of superspace methods can be found in the referenced material.
+ 5. The existing citations to references regarding the use of superspace coordinates and operators have been clarified in the new manuscript, including an explicit reference to an explanatory appendix on the method written by the author. Repeating the same content here seems unnecessary. The relationship between the right and left-hand sides of (37–39) were made using the elementary rules outlined in the aforementioned appendix and symbolic algebra software, with no other intermediate steps to share.
    * The subscript notation associated with the determinant has been explained in a footnote.