Before revision:  We think that this gives an almost complete description of the substitutive structure of Jeandel-Rao tilings  as we believe that \Omega_0\setminus X_0 is a null set for any shift-invariant probability measure on \Omega_0.
After revision:  We think that this gives an almost complete description of the substitutive structure of Jeandel-Rao tilings , as we believe that \Omega_0\setminus X_0 is a null set for any shift-invariant probability measure on \Omega_0.