(using means independent of RMT) to differentiate the two parities, and hence an extremely large number (see below) of possible ” s -wave” sets can be constructed from the observed resonances. 

Many different selections were applied to obtain the NDE. For example, in Ref. [2] it is stated that ”The criterion for inclusion in the NDE is that the individual sequences be in general agreement with the GOE.” Furthermore, data from many of the included nuclides were selected, at least in part, using measures derived from RMT for the GOE. 

Data for all but three of the 24 nuclides considered herein were obtained by the group at Columbia University. According to their publications (e.g., Ref.[19]), they had ”...no specific tests for s vs p levels, so there may be errors in these assignments.” Therefore, they relied on theoretical guidance, specifically measures derived from the GOE, to perform these separations. For example, for six of the 24 nuclides considered herein, including the two having the largest number of resonances, separation of p - from s -wave resonances was accomplished [39] by i) assuming all resonances having neutron widths larger than a certain (unspecified) size were s wave, ii) calculating the number of s -wave resonances below this size by assuming the PTD is correct, and iii) deciding which of the resonances below the threshold defined in the first step and needed to achieve the total number calculated in the second step, were s -wave by requiring good agreement with four spacing statistics (the Wigner nearest-neighboor spacing distribution, ρ ( S$_{j}$, S$_{j}$$_{+1}$ ), Δ$_{3}$, and the Dyson F test) derived from the GOE. Separation of s - from p -wave resonances for several of the other NDE nuclides followed the first two steps described above followed by a Bayesian analysis to decide which of the resonances below the threshold defined in the first step to assign to the s -wave set. The Bayesian analysis again assumes that the PTD is correct (for both s- and p -wave resonances) and furthermore requires the average widths for s - and p -wave resonances. The latter quantity usually is known only approximately, if at all. Such Bayesian analyses are known to be unreliable. For example, several neutron resonances in $^{64}$Zn [15] are known to be definitely p wave by their symmetrical shape in transmission (total cross section) data, but nevertheless have a Bayesian probability of > 99 % of being s wave. 

Given these selection procedures then, it is perhaps understandable that the NDE appears to agree well with the spacing statistics examined in Refs. [1, 2] despite that fact that the data are neither complete nor pure. Consider, for example, the case of $^{232}$Th, the NDE nuclide with the largest number of resonances. The authors of the primary reference from 

