KdV6: An integrable system

K2S2TK2S2T [A. Karasu-Kalkani, A. Karasu, A. Sakovich, S. Sakovich, R. Turhan, nlin/0708.3247] recently derived a new 6th-order wave equation KdV6: (∂x2+8ux∂x+4uxx)(ut+uxxx+6ux2)=0, found a linear problem and an auto-Bäckclund transformation for it, and conjectured its integrability in the usual sense. We prove this conjecture by constructing an infinite commuting hierarchy KdVn6 with a common infinite set of conserved densities. A general construction is presented applicable to any bi-Hamiltonian system (such as all standard Lax equations, continuous and discrete) providing a nonholonomic perturbation of it. This perturbation is conjectured to preserve integrability. That conjecture is verified in a few representative cases: the classical long-wave equations, the Toda lattice (both continuous and discrete), and the Euler top.