I bought some Whitney crab apples for pickling. I ate one prior, and it was fine. After I did the pickling, I cut a few open and there was a brown ring around the core of the seeds. Do you know what might have caused this?

The brown flesh around the core may have been caused by a fungus such as Alternaria sp.that entered through the calyx early in the fruit’s development. The condition, called moldy core, often cannot be detected until the fruit is harvested and cut. Here is a note about moldy core from the University of Massachusetts Apple Team:
“Moldy Core: This disease causes a rot with visible fungal growth in the seed cavity and core of some apple cultivars, particularly Delicious …