Also, Being a retired LEO, I’m thinking he could easily have given you a small break by writing for less than double over the limit, but I get the feeling he may have felt you needed a wake up call for whatever reason. Maybe he thought you weren’t taking it seriously enough or something. Or maybe he makes overtime for court.
Apologies if this rubs you the wrong way, but I think it's clear why it was 50 and not 49. The ticket for 25 over is 3X the fine that a ticket for 24 over would be. And, on review of the video, I was right around 50 when I came around that corner, so I'm sure that's what he got on his gun.
I didn't stop recording during the interaction with the officer, just so I had a record of it. I really don't think I was obnoxious, but it might have made him mad that I claimed I didn't see the signs. They were clear, no question at all; I didn't see them, but it's because I wasn't looking hard enough, not because they weren't there (or were obscured/etc). On the video, they are numerous and in the sight lines; when I reviewed the footage, I was stunned how obvious they were. Nobody knows if you're lying when you say "I didn't see it" except for you, so, to see how many signs there were that I completely missed...