I may be dumb, but I find : (sum_{i=1}^{n} x_i^2 + (n-2)*mu^2 ) / (n-1) instead of your (sum_{i=1}^{n} x_i^2 - n*mu^2 ) / (n-1).
However, everything is fine. It doesn't change the validity of the whole number and parity arguments.

Hi, thanks for the comment and sorry for the late reply! There is no mistake in the formula. What may be tripping you up is the fact that sum_{i=1}^{n} x_i is equal to n * mu (you seem to have assumed that it is equal to mu).

Hi Aurelien. This looks like a cool tool! Do you know if anyone else has used it and validated it yet? I'm interested in using for a project.

Hi Aaron! Thanks for the interest. No, I don't know anyone who has used it yet; in any case, as I note in the comments, impossible distributions can arise that wouldn't be caught with A-Grimmer, so using Sprite or Corvids is preferable. Let me know if you end up using it, and want to discuss it further!