Foul Ball or Foul Tip?

 
With a 0-2 count on the batter (B1) and no outs, the runner on first base (R1) is stealing on the pitch.
 
Even though the pitch is in the dirt and hits the ground, B1 swings and tips the pitch. The ball is tipped directly to the catcher's mitt, where it is secured, but the catcher's throw is late to second base, where R1 is safe.
 
Is this a foul ball (B1 remains at bat and R1 returns to first base) or a strike out (B1 is out and R1 remains at second base), or something else?
 
Call
A foul tip is a batted ball that goes sharply and directly to either the catcher's glove or the catcher's hand and then is legally caught by the catcher. It is a strike and the ball remains live (NF 2-16-1).
 
In the play below, even though the batter hit a pitch that had first struck the ground, he then tipped the ball to the catcher -- where all the criteria of a foul tip were met. This was the third strike, so the the batter is out, the ball remains live, and R1 remains at second base.