I don't mean to beat a dead horse, but I thought you'd be interested in this. It's a definition of "under the jurisdiction thereof" by the author of the 14th amendment, during the Senate debates on proposing the 14th amendment to the states:
"This amendment, which I have offered is simply declaratory ... that every person born within the United States, and subject to their jurisdiction is by virtue of natural law and national law a citizen of the United States. This will not of course include persons born in the United States who are foreigners, aliens, ..."
I understand, though my issue was more with the fact that Ted Cruz flip flopped on it without actually giving a reason for the flip flop. He was pretty clear in 2011 in his interpretation of the 14th.