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iPhones stored for forensic analysis unexpectedly reboot, causing problems for officials
(appleinsider.com)
This is a most excellent place for technology news and articles.
Could possibly also look at the motion sensors to see if it is in a pocket moving around or if it was sitting around for a while.
Good idea, but a motivated attacker could put them on one of those rocker tables like they use for mixing blood. It also wouldn't cover the more common scenario of someone stealing it out of your hand.