My car came with a CD with tire mfr's warranties on it. I haven't looked at them, hope I never need to. I'd be surprised though if road hazards are covered. Unfortunately, brand new tires are the ones most likely to pick up a nail or a screw in the tread. Patching the hole is problem-free. On the other hand, as others noted above, if you've driven on the tire while it was flat, or if the sidewall was damaged, it needs to be replaced.
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