I've pulled similar small nails out of my back tire on a few occasions and never had a problem.
One thing I've noticed about tire punctures: I've had maybe a half dozen over the last 20 years, and they were all in the back tire. My theory is that the front tire flicks nails laying on the ground upright, and then the rear tire gets stabbed.
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'14 Yamaha V-Star 650 Custom (silver)
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