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[53] We have also verified this with our simplified model of neutrino decoupling. 

[54] Here ν$_{3}$ is the lower-energy state, following the standard notation for the IH. 

[55] These two figures appear in Phys. Rev. Lett. as supple- mental online material, [52], because of space constraints. 

[56] This order-of-magnitude estimate omits O (1) factors. A more detailed analysis will be presented elsewhere. 

