1. Combine the cold water, sugar, and chopped pineapple in a large saucepan. Bring to a boil over medium-high heat, stirring until the sugar dissolves, then reduce heat to a steady boil and cook for 20 minutes, until the syrup is slightly thickened and the pineapple is very soft and translucent.
2. Remove from heat. Stir in the orange juice and lemon juice.
3. Allow the mixture to cool to room temperature, approximately 45 to 60 minutes, until no steam rises and the exterior of the pot feels cool to the touch.
4. Strain through a fine-mesh strainer or cheesecloth into a large pitcher or bowl, pressing gently on the solids to extract juice. Discard solids.
5. To serve, dilute with cold ice water to taste — begin with an equal volume of ice water and adjust for sweetness and strength. Serve over ice.
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