Word that means the classification of a number as even or odd

Solution 1:

Parity

  1. Mathematics (of a number) the fact of being even or odd.

(Oxford Dictionaries)

Solution 2:

What about simply evenness? I think this would require less explanation than parity. If you mentioned parity to a non-mathematical readership, you'd definitely have to explain what was meant.

According to Wiktionary, evenness means:

The quality of being even.

https://en.wiktionary.org/wiki/evenness

and obviously one of those meanings of even is the one you're referring to.