# Report #1

 * We fixed this typo.
 * The question of limits is a shrewd one, but ultimately the result is the same no matter how the calculation is done. Working directly at *M* = 1, the steps in the appendices are followed up to equation (28). With *M* = 1 and *V*₀² = *N**E*, the second term in the exponential remains of order *N* but the second is of order 1 and becomes another contribution to the prefactor. Comparing the resulting expression with (41) in the limit of α to zero with *V*₀² = *E*²/α, the two approaches result in the same effective action. In fact, an earlier version of this manuscript included two derivations, but the one for *M* of order 1 was deemed redundant in light of this. A note about this point has been added to the amended manuscript.
 * We agree, and further emphasized this in the amended manuscript.

# Report #2

 1. Ok, complex m^* solutions
 2.
 3.
 4. Maybe??

# Report #3

 1. Ok
 2. Ok
 3. Ok
   * The referee is wrong to say that the Euler characteristic of a hypersphere is 2 independent of dimension. The Euler characteristic of all odd-dimensional manifolds is zero. Consider the cell complex on *S*₁ [pictured here](https://kent-dobias.com/files/S_1.png). The Euler characteristic calculated using the alternating sum over the number of cells of increasing dimension is χ(*S*₁) = 1 – 1 = 0.
   * Ok
 4. Ok
   * Ok - discuss planting in manuscript, raise skepticism of results of fear paper.
 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.