We mention again that the smooth-neck Hamiltonian term, V neck (x), is not included in H aux . In this Appendix, we give an example (see Table ) of VFCI calculated expectation values that correspond to complete sets of the four integer quantum numbers that are expected from group theoretical considerations for the total spin and the total valley isospin. Deviations from the appropriate integer values, if any, appear at most at the fth decimal digit.