A smooth three-torus diffeomorphism with simple Lebesgue spectrum

We solve the probability-preserving form of Banach's simple Lebesgue-spectrum problem in smooth dynamics. We construct a C${}^{\infty }$ diffeomorphism of the three-torus that preserves standard volume and whose Koopman operator has simple Lebesgue spectrum on the entire mean-zero L${}^2$ space.