  N=4 supersymmetric string theories contain negative discriminant states whose
numbers are known precisely from microscopic counting formulae. On the
macroscopic side, these results can be reproduced by regarding these states as
multi-centered black hole configurations provided we make certain
identification of apparently distinct multi-centered black hole configurations
according to a precise set of rules. In this paper we provide a physical
explanation of such identifications, thereby establishing that multi-centered
black hole configurations reproduce correctly the microscopic results for the
number of negative discriminant states without any ad hoc assumption.
