  It was proposed that the tensor product structure of the Hilbert space is
uniquely determined by the Hamiltonian's spectrum, for most finite-dimensional
cases satisfying certain conditions.
  I show that any such method would lead to infinitely many tensor product
structures. The dimension of the space of solutions grows exponentially with
the number of qudits. In addition, even if the result were unique, such a
Hamiltonian would not entangle subsystems.
  These results affect the proposals to recover the 3d space from the
Hamiltonian.
