I typically run 38 PSI in the rear, but I had had this tire installed the day before, and the higher pressure I mentioned in the 1st post is how it was set. I had thought about checking it in the morning, but didn't. If this is all about running over something sharp, that's irrelevant. But if it's disappointing performance from a cold, new tire, I guess it could be a factor.
Cuts like that are common when a tire spins up and slides. It doesn't indicate that you ran over something sharp that made you fall down.
This scenario is a typical cold/new tire crash. You had the tire installed, didn't check the pressures, hadn't leaned it over very far on that side yet and had only ridden a half mile when you crashed. No tire is going to give its best grip under these conditions.
Your combination of lean angle and opening the throttle was too much for the condition at the moment. If you happened to be turning the throttle while adding lean angle, that can make a rear spin a lot sooner than if you set the lean angle before rolling on the gas.
The correction for this is to approach break-in and warmup with a little more caution. Scuff new tires gradually by progressively adding lean angle in successive turns. The contact patch in each of these turns should consist of some already scuffed rubber and some new. Be disciplined about this.
If you're in the habit of turning the bike quickly, turn in a little more slowly for the first few turns when tires are cold. If a tire slips, this makes it a little easier to catch than with a quicker turn-in. Once tires are warmer and you can predict traction, it's safe to turn more quickly.
Finally, be sure to separate turning in from rolling on the gas. Doing both at the same time is a time tested way to provoke a slide at much less lean angle than you would expect. Set the lean angle before you crack the throttle open.
It may ease your mind to replace the tire, but I think you'd come closer to addressing the cause if you correct some of the above.