  The Hauser-Feshbach Fission Fragment Decay (HF$^3$D) model is extended to
calculate the prompt fission neutron spectrum (PFNS) for the thermal neutron
induced fission on $^{235}$U, where the evaporated neutrons from all possible
fission fragment pairs are aggregated. By studying model parameter
sensitivities on the calculated PFNS, as well as non-statistical behavior of
low-lying discrete level spin distribution, we conclude that discrepancies
between the aggregation calculation and the experimental PFNS seen at higher
neutron emission energies can be attributed to both the primary fission
fragment yield distribution and the possible high spin states that are not
predicted by the statistical theory of nuclear structure.
