  Collective oscillations of supernova neutrinos swap the electron neutrino and
antineutrino spectra with those of another flavor in certain energy intervals
bounded by sharp spectral splits. This phenomenon is far more general than
previously appreciated: typically one finds one or more swaps and accompanying
splits in the neutrino and antineutrino channels for both inverted and normal
neutrino mass hierarchies. Depending on an instability condition, swaps develop
around spectral crossings (energies where the electron neutrino or antineutrino
fluxes are equal to that of another flavor, as well as infinite E where all
fluxes vanish), and the widths of swaps are determined by the spectra and
fluxes. Wash-out by multi-angle decoherence varies across the spectrum and
splits can survive as sharp spectral features.
