The Crook Point Bascule Bridge, abandoned for nearly 50 years over the Seekonk River, sits at a crossroads, costing the state $10,000 a month while the city of Providence tries to figure out a way to save what has become an unintentional local icon. The latest chapter of that effort: Mayor Brett P. Smiley is attempting to create a public authority that would maintain and redevelop the old train bridge, which has been stuck open since 1976.