Bring sugar and 1 cup water to a boil in a large saucepan. Cook, stirring occasionally, until sugar dissolves. Let syrup cool.
Pulse raspberries and remaining 3/4 cup plus 4 teaspoons water in a food processor until smooth. Strain through a fine sieve set in a deep bowl or a large glass measuring cup. Using a rubber spatula, gently press down on the mixture to extract as much liquid as possible; discard solids.
Transfer raspberry puree to a deep bowl or airtight container. Add syrup, and stir until well combined. Refrigerate for at least 1 hour.
Pour mixture into an ice cream maker, and freeze according to manufacturers' instructions. Transfer sorbet to a large airtight container, and freeze for at least 2 hours.
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