The pictured tire is a Continental GP4000 (23-622), almost brand new. The small circular divot next to the "V" shaped damage is one of the tread wear indicators on the tire. The tear doesn't penetrate the "Vectran" belt in the tire, but it does appear to go all the way to it.
I don't have much riding experience at this point so I'm curious from folks with a lot more miles under their belts what they would do. I've ridden about 50 miles on the tire since it was damaged (with a spare tire folded up and tucked in with my other gear). I've kept the tire at 100 PSI for those miles, and there's no visible bulging at that pressure.
I'd like to keep riding on it, given that it's almost new and it feels like a shame to replace it. My main concern is that it might blow out on me in some spectacular manner. Much beyond that, I'm fine with changing it on the side of the road instead of at my house if I have to.
EDIT: Sorry about the lighting, I took the photo with my cellphone in my basement, using my headlight to illuminate the tire.