My notes say that it's 0.527 OD, 40 pitch. But that's for a head that was done before I understood thread profiles as well as I do now, and I don't think I "really" understand thread profiles even yet.
It's a totally non-standard diameter for 40 pitch, so Cox could have made it to be whatever they wanted. If you're going to cut the threads, just cut & try (and remember to flatten the tops -- that's part of what I didn't understand about thread profiles when I made my notes).
It is 40 TPI, as are the threads on the .09.