which these data were taken [21, 39] state that 80% of the s -wave set (i.e. the set included in the NDE) were chosen to be s wave because they were too large to be p wave. Hence, 36 of the 178 $^{232}$Th resonances fall below this size and had to be selected as s wave using measures derived from the GOE, as noted above. In this same reference, 62 resonances are assigned as p wave (and hence by definition are below the s -wave threshold). Therefore, there are 98 resonances from which to choose the 36 needed to complete the s -wave set. Therefore, the number of possible s -wave sets is astronomically large (˜10 $^{27}$), and hence it should not be surprising that at least one set can be found to agree with the various RMT measures used in Ref. [39]. Similar numbers apply to the other data sets from Columbia. 

Finally, given that a significant fraction of the NDE data were selected using measures derived from RMT for the GOE, it seems highly questionable to use the full NDE for any test of this same theory. In contrast, the ” p -free” results presented herein circumvent this problem by eliminating these problematical resonances from the test. 

## VII. CONCLUSIONS 

I have shown that neutron widths in the NDE [2], when analyzed carefully, reject the PTD with high confidence. Given that reported deviations from the PTD for individual nuclides [21, 23, 40–44] have occurred on both sides of ν = 1, the statistical tests used herein likely underestimate the confidence with which the PTD can be rejected for the combined set of nuclides in the NDE. Furthermore, I have shown that the NDE is not pure and very likely incomplete. Also, measures derived from RMT for the GOE often were used in deciding which resonances to include in the NDE. These facts cast very serious doubt on repeated claims that the NDE constitutes a striking confirmation of RMT. 

Measurement techniques have improved considerably since the data in the NDE were acquired. In particular, new methods for determining resonance spins [44, 45] hold the promise of surmounting the difficulty of separating small s - from large p -wave resonances, which has been one of the most troublesome barriers to obtaining better data. Unfortunately most experimentalists continue to use RMT to correct their data for instrumental effects rather than use their data to test RMT. Exceptions to this practice are recent tests [23, 44] which have revealed significant disagreements between new neutron data and the PTD. These new data, together with previously reported disagreements [21, 40–43], which have 

