Artist Ilya Kabakov has breakfast at 7 a.m. every day. Emilia, his wife, a former world-class pianist, wakes up at 5 a.m. if she sleeps at all. She prepares her husband’s food in a kitchen with 20-foot-high wood-beam vaulted ceilings. Birds eat from metal feeders hanging from oak trees in the front yard. The soft waves of Peconic Bay sway against the shore down the hill.

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