You can correct the timer's error in this case because you had exact knowledge of the time involved. Put 4.1 seconds back on the clock and give the ball to the non-FT shooting team on the endline for another end-line throw-in. You can't give the ball to the non-throwing team at half-court because you don't have definite knowledge of how much time elapsed on the first throw-in.
NFHS rule 5-10-1.
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