Alan wondered about South's 4D rebid and so did I.
If you play Fit-Showing-Jumps ( FSJ), that is what 3C-jump would be.
Back in 2002, IanD made these comments:
FSJ on :
a) In competition (including over a DBL ) and
b) as a passed hand .
He went on to say from experience:
"Actually the bid comes up more often over a minor suit opening ! !, and, again as you suggested, this shows at least a 5 card suit with at least 4 card support for the minor. "