What is the appropriate response to a jump rebid by responder under Standard American?
I agree in part and disagree in part with Forget. The Standard American system booklet indicates that responder's rebid of a suit at the three level is invitational, not forcing. However, your hand is a maximum for your rebid, and therefore you should accept the invitation.

While visualizing the kinds of hands partner might have is a useful exercise, particularly for slam bidding, (a) you have to visualize a half dozen or so different hands to draw useful conclusions rather than finding just one, and (b) it's probably not valuable enough to justify the energy expenditure when you're making a 3- vs 4-level decision with a run-of-the-mill balanced hand.