How to Make It
In a bowl, mix the warm water and yeast; let stand until foamy, 5 minutes. Stir in the cold water, 3 tablespoons of the all-purpose flour and the rye flour. Cover and let stand until bubbly, 30 minutes.
Stir in the remaining 2 1/4 cups of flour, the olive oil and salt. Turn the dough out onto a lightly floured work surface and knead until soft and smooth. Transfer the dough to a large oiled bowl, cover with plastic wrap and let stand until doubled in bulk, about 1 1/2 hours.
Preheat the oven to 500° and set a pizza stone on the bottom of the oven. On a floured work surface, punch the dough down and divide into thirds. Shape each piece into a ball. Cover 2 pieces with plastic wrap and let stand for 15 minutes. Wrap the remaining piece in plastic and freeze for later use.
In a small bowl, combine the garlic with the lemon juice and mayonnaise. Season the aioli with salt.
In a medium skillet, heat the 1 tablespoon of olive oil. Add the onion, cover and cook over moderate heat, stirring occasionally, until softened, 8 minutes. Season with salt.
Generously flour a pizza peel. On a lightly floured work surface, roll out or stretch 1 ball of dough to a 12-inch round. Transfer the round to the pizza peel and brush the dough with olive oil. Scatter half of the onion, tomatoes and tuna over the pizza and slide onto the hot stone. Bake the pizza for about 7 minutes, until crisp and bubbling. Remove from the oven and drizzle the pizza with half of the aioli. Top with half of the basil and arugula, cut into wedges and serve. Repeat with the remaining dough and toppings.