They want proof. Baby boxes — temporary cardboard bassinets — are booming among new parents. Following Finland’s example, some states are giving the supplies-laden cartons to expectant mothers to promote safer sleep. Proponents say the boxes’ firm mattresses and compact size help prevent sleep-related deaths, but the American Academy of Pediatrics warns of unanswered questions about potential bacterial growth and the safety of box adhesives. While consumer safety groups test the boxes, low Finnish infant mortality rates and increased awareness of newborns’ needs may help parents sleep more soundly.