Fed says (probably renumbered since my edition, was 2-27-5):
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The line to gain is the yard line established when a new series (first down) is awarded. Unless there is a penalty following the ready-for-play signal, the line to gain is 10 yards in advance of the foremost point of the ball when placed for the first down of the series.
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NCAA says substantially the same thing at 5-1-2(b):
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The line to gain is established when the ball is made ready for play before the first down of the new series.
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and amplifies at 5-2-7(a):
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The penalty for any dead-ball foul (including live-ball fouls treated as dead-ball fouls) that occurs after a series ends and before the ball is ready for play shall be completed before the line to gain is established.
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So considering the likely timing of the sequence you describe -- UC foul occurring during the dead ball interval before the new line-to-gain was marked -- it'd be 1st & 10.