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Question
After ball 4,catcher throws to pitcher on the rubber before runner gets to first.Can she still round and go to 2nd base without hesitation?

Answer
Yes, absolutely.  The pitcher having control of the ball in the circle doesn't stop the runner.  If the runner does stop, they must immediately commit to a base.  Once they have committed to a base, they must continue to go to that base unless the pitcher starts to make a play.  There are some other things to look at with this for example, if the runner over runs first base, with the ball under the pitchers control in the circle, then heads back to first base (committing to the base) then turns and runs to second with out any hesitation, the runner is out.  If she simply rounds first and keeps going to second, there is no problem with that.