[noone_important]

I agree, that neutrinoless double beta decay would be incredibly interesting, but it is very speculative (and depending on the neutrino mass hierarchy not really falsifiable).

My original point was just that lepton number is not a good symmetry as it is broken by rhe chiral anomaly, which is not speculative at all. Of course, the sphaleron effects are negligible in collider settings, but for cosmology they are crucial and might be indirectly observable.