About six million Americans receiving food stamps report they have no other income, according to an analysis of state data collected by The New York Times. In declarations that states verify and the federal government audits, they described themselves as unemployed and receiving no cash aid no welfare, no unemployment insurance, and no pensions, child support or disability pay. Their numbers were rising before the recession as tougher welfare laws made it harder for poor people to get cash aid, but they have soared by about 50 percent over the past two years. About one in 50 Americans now lives in a household with a reported income that consists of nothing but a food-stamp card. Members of this straitened group range from displaced strivers ... to weathered men who sleep in shelters and barter cigarettes. Some draw on savings or sporadic under-the-table jobs. Some move in with relatives. Some get noncash help, like subsidized apartments. While some go without cash incomes only briefly before securing jobs or aid, others rely on food stamps alone for many months. The surge in this precarious way of life has been so swift that few policy makers have noticed. But it attests to the growing role of food stamps within the safety net. One in eight Americans now receives food stamps, including one in four children.