Next day, it was still there, in the same spot, apparently not having moved at all.
Day after that, August 26, this is what I found:
What you see in the picture is the caterpillar above and its castoff exoskeleton rolled up below. I knew that caterpillars shed their skins a few times before they were ready to move on to the next stage, but somehow didn't picture fuzzy ones such as this shedding them whole, like peeling off a fur coat to reveal another underneath.
The day after the last shot the caterpillar was gone--then later I saw a quite lively dagger moth caterpillar motoring across the front porch and into the front garden, a cat with purpose! Cindy of Woodsong has a good picture of the moth this one will be turning into here.