From d017d9982e121258b86d435a00eda55138a0e16b Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Fri, 7 Feb 2025 18:28:31 -0300 Subject: Began to write referee responses. --- referee_response.md | 21 ++++++++++++++++++++- 1 file changed, 20 insertions(+), 1 deletion(-) diff --git a/referee_response.md b/referee_response.md index 51e7f85..b58e21c 100644 --- a/referee_response.md +++ b/referee_response.md @@ -1,5 +1,24 @@ # 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. -- cgit v1.2.3-70-g09d2