[en] A new prompt fission neutron spectrum matrix for the n+²³⁵U system is proposed. The thermal neutron spectrum is this matrix describes the newest data of JRC IRMM by Hambsch et al. (2009). The longstanding problem of inconsistency of integral thermal data testing and differential prompt fission neutron spectra data (PFNS) seems to be solved. It was mostly due to rather poor fits of differential PFNS data in major data libraries. The older measured database is updated here using modern standards like spontaneous fission neutron spectra of ²⁵²Cf(sf). That largely removes the inconsistency of older thermal neutron-induced PFNS data with the newest data. A phenomenological approach, developed by Kornilov et al. (1999), for the first-chance fission and extended for the emissive fission domain by Maslov et al. (2005) is normalized at E_th to predict both the PFNS average energy < E> and PFNS shape up to 20 MeV. In the first-chance and emissive fission domain evaluated PFNS are consistent with the < E> data by Ethvignot et al. (2005). A compiled ENDF/B-formatted file of the ²³⁵U(n,F) PFNS largely removes the inconsistencies of the evaluated differential PFNS with integral data benchmarks. Fast integral critical experiments like GODIVA or Flattop benchmarks are reproduced with the same accuracy as with the PFNS of the major data libraries. That reveals a rather delicate compensation effect, since present and previous PFNS shapes are drastically different from each other. Thermal assembly benchmarking reveals positive biases in k_eff, which might be attributed to the influence of a soft energy tail of the present PFNS. For some of Valduc's LCT benchmarks biases in k_eff are less than 20 pcm. (authors)