  The indefinite sign of the Hamiltonian constraint means that solutions to
Einstein's equations must achieve a delicate balance--often among numerically
large terms that nearly cancel. If numerical errors cause a violation of the
Hamiltonian constraint, the failure of the delicate balance could lead to
qualitatively wrong behavior rather than just decreased accuracy. This issue is
different from instabilities caused by constraint-violating modes. Examples of
stable numerical simulations of collapsing cosmological spacetimes exhibiting
local mixmaster dynamics with and without Hamiltonian constraint enforcement
are presented.
