Texas surpassed 500,000 confirmed coronavirus cases Tuesday as Republican Gov. Greg Abbott suggested family and neighborhood gatherings are behind a sharp rise in the rate of positive tests, which has climbed to record levels just as schools are beginning to reopen across the state. He also continued to say more testing in Texas is likely after dropping off in recent weeks, a trend seen across the U.S. even as deaths mount. Texas has reported more than 1,400 new deaths over the past week, including 220 on Tuesday. Although health officials say there are encouraging signs in Texas — particularly hospitalization levels that have dropped more than 30 percent since July’s peak — infection rates have been on a steady increase.