  The tridecompositional uniqueness theorem of Elby and Bub (1994) shows that a
wavefunction in a triple tensor product Hilbert space has at most one
decomposition into a sum of product wavefunctions with each set of component
wavefunctions linearly independent. I demonstrate that, in many circumstances,
the unique component wavefunctions and the coefficients in the expansion are
both hopelessly unstable, both under small changes in global wavefunction and
under small changes in global tensor product structure. In my opinion, this
means that the theorem cannot underlie law-like solutions to the problems of
the interpretation of quantum theory. I also provide examples of circumstances
in which there are open sets of wavefunctions containing no states with various
decompositions.
