Consistency around a cube property of Hirota's discrete KdV equation and the lattice sine-Gordon equation

It has been unknown whether Hirota’s discrete Korteweg-de Vries equation and the lattice sine-Gordon equation have the consistency around a cube (CAC) property. In this paper, we show that they have the CAC property. Moreover, we also show that they can be extended to systems on the 3-dimensional integer lattice.