The resident contacted DSNY after realizing the rings were gone. Crews pulled a truck from the department’s Brooklyn South 13 District before it reached its usual destination and redirected it to a waste management facility on Varick Street instead, a DSNY official said. The catch: DSNY can supervise a search, but it’s up to the caller to dig through the truck’s contents themselves. “People know their trash very well,” Goodman said, noting the searches often succeed. Goodman’s advice for anyone who suspects they’ve tossed something valuable: call 311 immediately — even an hour’s delay can matter.