If police validly hold someone outside their home in order to quickly get a search warrant, is this an arrest or detention?

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Temporary restraint for a specific investigative purpose is detention. In this scenario, police are not taking the person into custody for charging them with a crime or transporting them to jail. They are briefly restricting movement outside the home to facilitate obtaining a search warrant. That kind of short-lived, purpose-limited interference with liberty fits the concept of detention rather than an arrest, which would involve formally taking someone into custody and typically proceeding toward charges or booking. Custody and seizure are broader terms for being under police control, with custody often associated with interrogation or after an arrest, and seizure referring to any meaningful interference with liberty. So the appropriate description here is a brief detention.