Who was the wise guy that said this was a Cadet Hat?
Answer: Myself for sure, and maybe a couple of others.
As I alluded to earlier, we know this type of hat was fairly common around the turn of the century, and was worn by a variety of people from cadets to band members.
I also discoverd the style is referred to as a "Bell Crown" hat/cap.
The image below is of a 1923 Band cap.
Notice the similarity of the "ribbing" and embrodery on the upper brow area.
I am not trying to confuse anyone, but rather suggesting we look in a wide variety of other areas. Especially when you consider the fact that no one has yet found a single Pennsylvania school that fits the letters D S C. But there may very well be Town Bands, Police Departments, Fire Departments, Telegraph Offices, etc. that do work with the letters. I guess this is a case of thinking outside of the box. Or, if you prefer, just another dumb guess.
P.S. Despite the logo with the image, they claimed this was an original, vintage cap.
Also, not all of the band caps I've seen have a "B" on the end for "Band."
BOTTLE"CAP"BOB