  Truncated sum rules have been used to calculate the fundamental limits of the
nonlinear susceptibilities; and, the results have been consistent with all
measured molecules. However, given that finite-state models result in
inconsistencies in the sum rules, it is not clear why the method works. In this
paper, the assumptions inherent in the truncation process are discussed and
arguments based on physical grounds are presented in support of using truncated
sum rules in calculating fundamental limits. The clipped harmonic oscillator is
used as an illustration of how the validity of truncation can be tested; and,
several limiting cases are discussed as examples of the nuances inherent in the
method.
