1. In order to conform with the note, all use of 'log' in our manuscript should be replaced with 'ln'. These appear on lines 10 (twice), 116, 118, the equation between lines 173 and 174, twice in equation (12), twice in equation (13), twice in the caption of Fig. 2, twice in equation (15), twice in equation (16), and twice in equation (17).

2. If we must use section headings, here are our preferences:

  Between lines 16 and 17: Introduction

  Between lines 135 and 136: Calculation

  Between lines 210 and 211: Results

3. Yes.

4. The article was published online 15 October 2014, but the issue of International Mathematics Research Notes (IMRN) containing it was published in 2015. IMRN recommends the article be cited with the year 2015, and this is what is in the DOI database.

Q. Links to details for the marked citations follow:

  [2] Zeitschrift für Physik B Condensed Matter volume 87, pages 341–354 (1992)
  https://link.springer.com/article/10.1007%2FBF01309287

  [10] J. Phys. I France 5 (1995) 805-813
  https://jp1.journaldephysique.org/articles/jp1/abs/1995/07/jp1v5p805/jp1v5p805.html

  [18] Proceedings of The 33rd International Symposium on Lattice Field Theory — PoS(LATTICE 2015) volume 251, page 16 (2016)
  https://pos.sissa.it/251/016/

Other comments:

  Lines 26, 27 (twice), 114, 120, 169, and 199: the en dashes separating concatenated names have been removed and replaced with hyphens. We prefer that concatenated names be separated by en dashes, as they appeared in the submitted manuscript. How is one to interpret "Kent-Dobias" printed next to "Fadeev-Popov"? Are there two or three authors behind a technique due to "Kent-Dobias-Kurchan"?

  Line 14: the fragment "the square root of the total number of solutions is real" should read "the square root of the total number of solutions are real". The word "real" is describing the solutions, which are plural, not the square root of the total number.

  Equation (5): the "r" should be capitalized in "N(κ, ε, r)", or "N(κ, ε, R)".

  Line 142: the sentence "The results of these calculations begin around (15)." should be removed, as it is unnecessary if we are forced to use section headings.

  The equation between lines 173 and 174: please add an equation number to this equation, and increment the equation numbers (and their references) of all equations that follow.