I'm pretty overwhelmed with the kind responses and encouragement here, thank you all. I'm looking at the bowl a little differently now since before I was mostly just seeing something that did not explode while I was turning it and instead made it into a bowl shape

It was beginner's luck that it survived.
To answer the questions - I actually thought it was light coming through the sides when I was taking the picture and prior, when it was on a table with light coming in from a window, but no, it is actually the light reflecting off the other inside wall. Really odd that it looks that way in the photo and in person. That's what made me knock together a double-s caliper and measure the side, thinking it couldn't be
that thin! (it wasn't

)
As for the grain, the pith would be just outside the bowl, under the bottom. It makes for a pretty crazy wave all around, and the wood changes color oddly perpendicular to the grain. Oh, just looked at the photo and it doesn't show that coloring much at all, just the slight figure that is there in some angles. The pith in the photo runs parallel to the edge of the thing it is sitting on (that would be the microwave, as the kitchen window had nice light, hence the cloth. It was either that or wipe down the top of the microwave).
About the shopsmith as a lathe (remember I've made one bowl so far!) - I had trouble when I first started the bowl a while ago and roughed out the inside. It wasn't much fun and I stopped, all because it seemed too flexible and hard to control. This time I'd read a bit first (novel idea) and did not have it very tightly pressed against the live center. Go figure, the tailstock no longer flexed out wearisomely. I also ran it faster, which was much more comfortable, if a bit more scary. The main trouble I had was the tool rest not reaching anywhere close for some cuts using the tailstock but it worked out. I did notice my neck after finishing so I need to figure out a way to raise and lower the whole thing.
Oh, I know, it also didn't vibrate as much because I left the planer on the far side of the headstock. Next time I might leave the jointer on as well. Then again, I'd already roughed it down to round.
Thanks again for the supportive comments.