I'm referring here to the significance estimates of section 3. It's immediately suspicious that the authors introduce a new type of "test" for whatever spectra

I'm referring here to the significance estimates of section 3. It's immediately suspicious that the authors introduce a new type of "test" for whatever spectra are being measured. When that happens, the authors need to rigorously demonstrate its validity. That is not present in this preprint. The thing that needs to be demonstrated is that their method generates a reasonable space of outcomes. It's not clear to me that's true for their method.