Dr. Pepper-
I’ll b’n give it a shot, but your challenge is quite likely beyond my math skill level (& smarts). I need some time, though, so some other math maven may rescue me – ..er I mean beat me to the solution in the meantime.
I agree with “The Big One” that you come across as older than you are for several reasons: 1) A math PhD is more common among older folks (like me, but sans degree). 2) Your experience as a teacher 3) Your style of speech is more comfortable and mature, and less “reactionary” than some younger posters. 4) Precise word usage, accurate grammar and accurate word spelling.
The fact that you B”H just had a mazel tov clued me in that you were a bit younger than my first impression. If I had to, I’d guess that this is your first (you mentioned the nachas you and your wife are B”H having, but not sibling reactions, as well as a detail or two first-time parents focus on more), but I’ve been wrong before.