ź-bounds consistency for the spread constraint with variable mean

The spread constraint enforces a relationship amongst a set of variables, their mean, and their standard deviation. The ź-bounds consistency (BC) algorithms that have been formally published and the implementations of which we are aware all assume a fixed mean value. A sketch of the BC algorithm with variable mean was proposed, which relies on the continuity property of a key function used in the fixed mean case. We show that this function may be piecewise discontinuous, meaning that the extension of the algorithm to the variable mean case that is suggested in the literature is unsound. We propose a simple modification of the algorithm that achieves ź-BC with variable mean.