Calculating a Luhn Check Digit
All in all it seems OK to me. A couple of things though:

1) 

  const int validCodePointCount = 10;
  const int validCodePointOffset = 48;


The names of these constants are hard to distinguish from each other and to understand in the context and they blur the behavior of the algorithm.

Better names could be:

const int numberBase = 10;
const int zero = '0';


Here I use '0' instead of 48 because the first is much more recognizable to programmers than the latter, and we instantly grasp the meaning. In fact in such a relatively small algorithm, I would prefer to use the literals directly in the code than the named constants like: 

var digit = (value[index] - '0');


This is such a common operation and we all know what it's about immediately when seeing it.

In general it is wise to avoid magic numbers, but in some situations it is preferable in order to improve readability - IMO.



2)

You don't have to iterate backwards because you can determine the initial parity from the length of the input string:

var parity = value.Length % 2 != 0;


You can then iterate forward:

foreach (int n in value.Select(c =&gt; c - '0'))
{
  ...
  parity = !parity;
}