In large mixing bowl, combine 1/2 teaspoon yeast and 1/2 cup warm water. Let sit until yeast dissolves, about 1 minute. Stir in 3/4 cup white flour, cover with plastic wrap and set aside 2 hours.
Gently stir in remaining 2 cups water, remaining 1/2 teaspoon yeast, remaining white flour and salt. Add mashed potatoes, rye flour and wheat flour, incorporating flours 1 cup at a time until you have a dough that is soft and pliable, but firm enough to handle.
If you’re kneading by hand, turn dough out onto a lightly floured surface and knead until smooth, about 10 minutes. (It helps to moisten your hands while you knead.) If you’re using an electric mixer with a dough hook, knead by machine until dough pulls away from bowl and forms a ball around the hook.
Add additional flour only if absolutely necessary to prevent sticking. Let dough rest while you wash out mixing bowl. Lightly oil mixing bowl, place dough in bowl and turn over to coat both sides with oil. Cover with kitchen towel; set aside until doubled in bulk, about 1 1/2 hours.
Preheat oven to 425°F. Punch down dough and knead lightly to press out air. Turn out onto lightly floured surface. Sprinkle dough with caraway seeds and knead until dough is elastic and seeds are well distributed, about 4 minutes.
Shape dough into round loaf about 9 inches in diameter; place on baking sheet dusted with cornmeal. Cover with kitchen towel and let rise about 40 minutes. Slash an “X” into top of loaf with sharp knife.
Bake until top is browned and bread sounds hollow when tapped on bottom, about 1 hour. Cool on wire rack about 15 minutes before slicing.