The most significant case in decades on homelessness has reached the Supreme Court as record numbers of people in America are without a permanent place to live. The justices on Monday will consider a challenge to rulings that found punishing people for sleeping outside when shelter space is lacking amounts to unconstitutional cruel and unusual punishment. A political cross-section of cities in California and across the West argue the decision has restricted them from “common sense” measures intended to keep homeless encampments from taking over public parks and sidewalks. Advocacy groups say the ruling provides essential legal protections, especially with an increasing number of people forced to sleep outside as the cost of housing skyrockets.