those built on the ground state. This hypothesis allows to express the probability of the $\gamma$ decay in the statistical regime as being proportional to a separable product of the final-state level density and the RSF. Although the Brink assumption can be questionable, in particular from the point of view of some models such as the Fermi liquid theory [@ka83], it should be emphasized that the presence of the upbend structure has been tested against such an assumption. Specifically, the RSFs for $^{56,57}$Fe [@Fe_Alex], $^{96,98}$Mo [@Mo_RSF], and $^{45}$Sc [@Sc] have been determined for various initial energies and shown to present the upbend structure for all the excitation bins studied. From such a test, it can be inferred that the eventual temperature-dependence of the RSF at low energy is small with respect to the strength of the upbend structure. In this low-energy region, the validity of the Brink hypothesis remains a fundamental open question.

Uncertainties in the subtraction procedure of the Oslo method, including the estimate of the statistical multiplicity have also been studied in [@Mo_reanalyzed] and shown not to affect the RSF significantly and definitely not the conclusion regarding the existence of the upbend pattern.

Finally, it should also be 