Dear authors,

I think that the paper is now almost ready for publication. I have listed some technical issues that might help to make the paper better readable. I leave the decision to you if you want to include my suggestions or not.

Cheers,
Thomas

Title: I suggest to remove the abbreviation (HRTP) from the title.

Abstract: Wouldn't it be adequate to introduce the abbreviation HRTP in line 10, not only in line 16?

Personally, I would prefer to avoid line breaks in the abstract.

Intro: l35 I suggest to avoid "would like to"; just write "we give a precise definition of what..."

p3 l4 but with A slightly.. and A different discretization...

p3 l5 it has BEEN shown (?)

p8 l13 and elsewhere: I am not sure if the term "filtration" is adequate for application of a mathematical filter. All examples of "filtration" I have found refer to physical filtering. Probably the term "filtering" might be more adequate than the term "filtration" in your context. Could you check with a native English speaker about this?

p9 l4 Gaussian distributionS

p11 l10 requires A monotonous (add article). By the way: I think 'monotonous' means something like 'boring', or the opposite of `diversified'. The mathematical technical term is 'monotone' or 'monotonic'. Is 'impact parameter' a technical term in the context of Abel integration? Or do you mean 'input parameter'?

Please indicate somewhere how the error estimates are to be understood. E.g., you could write at the appearance of the first error estimate "(all error estimates in this paper are plusminus one sigma)" or something like this.