Place sugar, water, syrup, and salt in a heavy saucepan; insert candy thermometer.
Heat and stir over moderate heat until sugar dissolves, reduce heat slightly, and cook uncovered without stirring to 240° F.
Remove from heat, stir in nuts, and pour onto a wax-paper-lined baking sheet.
Spread out as thin as possible and let cool until hard.
Break apart, separating into individual nuts.