Justice Schack, like a handful of state and federal judges, has taken a magnifying glass to the mortgage industry. In the gilded haste of the past decade, bankers handed out millions of mortgages — with terms good, bad and exotically ugly — then repackaged those loans for sale to investors from Connecticut to Singapore. Sloppiness reigned. So many papers have been lost, signatures misplaced and documents dated inaccurately that it is often not clear which bank owns the mortgage. Justice Schack’s take is straightforward, and sends a tremor through some bank suites: If a bank cannot prove ownership, it cannot foreclose. Justice Schack’s duels with the banks started in 2007 as foreclosures spiked sharply. He saw a plague falling on Brooklyn, particularly its working-class black precincts. “Banks had given out loans structured to fail,” he said.