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Miranda rights don’t need to be read until the person in question is under arrest.
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If it was on his person at the time of his arrest, then they can search it without a warrant.
You don’t have to agree with the prosecution of Mangione but critiquing procedure a faux-legalistic perspective does nobody any good.
Identity, where’d he been, his ID, don’t constitute “interrogation” for the purpose of Miranda rights.
That’s more or less true, but he didn’t ask, “Am I under arrest.”