  The counting function on binary values is extended to the signed case in
order to count the number of transitions between contiguous locations. A
generalized subdifferential for the sign change counting function is given
where classical subdifferentials remain intractable. An attempt to prove global
optimality at some point, for the 4-dimensional first non trivial example, is
made by using a sufficient condition specially tailored among all the cases for
this subdifferential.
